Multi-phase coriolis flowmeter

ABSTRACT

A flowmeter is disclosed. The flowmeter includes a vibratable flowtube, and a driver connected to the flowtube that is operable to impart motion to the flowtube. A sensor is connected to the flowtube and is operable to sense the motion of the flowtube and generate a sensor signal. A controller is connected to receive the sensor signal. The controller is operable to determine an individual flow rate of each phase within a multi-phase flow through the flowtube.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. §119(e) to U.S.Application Ser. No. 60/549,161, filed on Mar. 3, 2004, and titledMULTIPHASE CORIOLIS FLOWMETER. Under 35 U.S.C. §120, this applicationclaims priority to, and is a continuation of U.S. application Ser. No.11/069,931, which is a continuation-in-part of, U.S. application Ser.No. 10/773,459, filed Feb. 9, 2004, and titled MULTI-PHASE CORIOLISFLOWMETER, which itself claims priority under 35 U.S.C. §119(e) to bothof (i) U.S. Application Ser. No. 60/445,795, filed on Feb. 10, 2003, andtitled MULTIPHASE CORIOLIS FLOWMETER and (ii) U.S. Application Ser. No.60/452,934, filed on Mar. 10, 2003, and titled MULTIPHASE CORIOLISFLOWMETER. All of the above-listed applications are hereby incorporatedby reference.

TECHNICAL FIELD

This description relates to flowmeters.

BACKGROUND

Flowmeters provide information about materials being transferred througha conduit, or flowtube. For example, mass flowmeters provide anindication of the mass of material being transferred through a conduit.Similarly, density flowmeters, or densitometers, provide an indicationof the density of material flowing through a conduit. Mass flowmetersalso may provide an indication of the density of the material.

For example, Coriolis-type mass flowmeters are based on the Corioliseffect, in which material flowing through a conduit is affected by aCoriolis force and therefore experiences an acceleration. ManyCoriolis-type mass flowmeters induce a Coriolis force by sinusoidallyoscillating a conduit about a pivot axis orthogonal to the length of theconduit. In such mass flowmeters, the Coriolis reaction forceexperienced by the traveling fluid mass is transferred to the conduititself and is manifested as a deflection or offset of the conduit in thedirection of the Coriolis force vector in the plane of rotation.

SUMMARY

According to one general aspect, a system includes a controller that isoperable to receive a sensor signal from a first sensor connected to avibratable flowtube containing a three-phase fluid flow that includes afirst liquid, a second liquid, and a gas, the controller being furtheroperable to analyze the sensor signal to determine an apparent flowparameter of the fluid flow, a second sensor that is operable todetermine an apparent flow condition of the fluid flow, and acorrections module that is operable to input the apparent flow parameterand the apparent flow condition and determine a corrected flow parametertherefrom.

Implementations may include one or more of the following features. Forexample, the corrections module may be further operable to input theapparent flow parameter and the apparent flow condition and determine acorrected flow condition therefrom. The apparent flow parameter mayinclude an apparent bulk density of the fluid flow, or an apparent bulkmass flow rate of the fluid flow.

The second sensor may include a liquid fraction probe that is operableto determine a liquid fraction measurement identifying a volume fractionof the first liquid with respect to the second liquid, or a voidfraction determination system that is operable to determine a voidfraction of the gas within the fluid flow.

A component flow rate determination system may be included that isoperable to determine a flow rate of the first liquid within the fluidflow. The component flow rate determination system may be implemented atthe controller, the corrections module, the second sensor, or a hostcomputer in communications with the controller, the corrections module,or the second sensor.

A component flow rate determination system may be included that isoperable to determine a flow rate of the gas within the fluid flow.Implementation of the corrections module may be associated with aprocessor of the controller, or with a processor of the second sensor. Ahost computer may be in communication with the controller or the secondsensor and operable to implement the corrections module.

In the system, the second sensor may be operable to output a firstapparent flow condition value to the controller for use in determinationof a first corrected flow parameter value, and the controller may beoperable to output the first corrected flow parameter value to thesecond sensor for determination of a first corrected flow conditionvalue, and the second sensor may be operable to output a secondcorrected flow condition value to the controller for use indetermination of the corrected flow parameter value.

The correction module may include a neural network that is operable toinput the apparent flow parameter and the apparent flow condition andoutput the corrected flow parameter and a corrected flow condition. Theneural network may include a first correction model that is particularto a type of the second sensor and flow condition and that is operableto output a corrected flow condition, and a second correction model thatis particular to a type of the apparent flow parameter and that isoperable to output the corrected flow parameter, wherein the firstcorrection model may be operable to correct the apparent flow conditionbased on the apparent flow condition and the corrected flow parameter,and the second correction model may be operable to correct the apparentflow parameter based on the apparent flow parameter and the correctedflow condition.

The controller may be operable to correct the apparent flow parameterbased on a theoretical relationship between the apparent flow parameterand the corrected flow parameter. The controller may be operable tocorrect the apparent flow parameter based on an empirical relationshipbetween the apparent flow parameter and the corrected flow parameter.

The system may include a conduit connecting the second sensor and thevibratable flowtube, such that the fluid flow flows through the secondsensor, the pipe, and the vibratable flowtube. The first liquid, thesecond liquid, and the gas may be co-mingled with one another within thefluid flow during determination of the flow condition by the secondsensor.

According to another general aspect, an apparent bulk density of amulti-phase flow through a flowtube is determined, the multi-phase flowincluding a first liquid, a second liquid, and a gas. An apparent bulkmass flow rate of the multi-phase flow is determined, and a first massflow rate of the first liquid is determined, based on the apparent bulkdensity and the apparent bulk mass flow rate.

Implementations may include one or more of the following features. Forexample, an apparent flow condition of the multi-phase flow other thanthe apparent bulk density and the apparent bulk mass flow rate may bedetermined, wherein determining the first mass flow rate of the firstliquid comprises determining the first mass flow rate based on theapparent flow condition. In determining the first mass flow rate of thefirst liquid, a corrected flow condition may be determined, based on theapparent flow condition. In determining the corrected flow condition, acorrected bulk density and a corrected bulk mass flow rate may bedetermined.

Determining the apparent flow condition may include determining anapparent liquid fraction measurement of a volume fraction of the firstliquid within the multi-phase flow, and/or determining an apparent gasvoid fraction of the gas within the multi-phase flow.

Determining the first mass flow rate of the first liquid may includedetermining a corrected bulk density, based on the apparent bulkdensity, and determining a corrected bulk mass flow rate, based on theapparent mass flow rate. Determining the corrected bulk density anddetermining the bulk mass flow rate may include determining a correctedflow condition, based on the apparent flow condition.

According to another general aspect, a flowmeter includes a vibratableflowtube containing a three-phase flow including a first liquid, asecond liquid, and a gas, a driver connected to the flowtube andoperable to impart motion to the flowtube, a sensor connected to theflowtube and operable to sense the motion of the flowtube and generate asensor signal, and a controller connected to receive the sensor signaland determine a first flow rate of a first phase within a three-phaseflow through the flowtube, based on the sensor signal.

According to another general aspect, a method of improving an output ofa flowmeter includes determining an apparent bulk density of amulti-phase flow through a flowtube, the multi-phase flow including afirst liquid, a second liquid, and a gas, determining an apparent bulkmass flow rate of the multi-phase flow, determining an apparent flowcondition of the multi-phase flow, and correcting the apparent bulkdensity or the apparent mass flow rate, based on the apparent bulkdensity, the apparent mass flow rate, and the apparent flow condition.

According to another general aspect, a method of improving an output ofa liquid fraction probe includes determining an apparent bulk density ofa multi-phase flow through a flowtube, the multi-phase flow including afirst liquid, a second liquid, and a gas, determining an apparent bulkmass flow rate of the multi-phase flow, determining an apparent liquidfraction the first liquid within the multi-phase flow, and correctingthe apparent liquid fraction to obtain a corrected liquid fraction,based on the apparent bulk density, the apparent mass flow rate, and theapparent liquid fraction.

Implementations may include one or more of the following features. Forexample, a gas void fraction of the gas within the multi-phase flow maybe determined based on the apparent bulk density, the apparent mass flowrate, and the corrected liquid fraction.

According to another general aspect, a method of obtaining a gas voidfraction measurement includes determining an apparent bulk density of amulti-phase flow through a flowtube, the multi-phase flow including afirst liquid, a second liquid, and a gas, determining an apparent bulkmass flow rate of the multi-phase flow, determining an apparent gas voidfraction of the gas within the multi-phase flow, and correcting theapparent gas void fraction to obtain a corrected gas void fraction,based on the apparent bulk density, the apparent mass flow rate, and theapparent gas void fraction.

Implementations may include one or more of the following features. Forexample, a liquid fraction of the first liquid within the multi-phaseflow may be determined based on the apparent bulk density, the apparentmass flow rate, and the corrected gas void fraction

According to another general aspect, a system includes a conduit havinga fluid flow therethrough, the fluid flow including at least a firstliquid component, a second liquid component, and a gas component, avibratable flowtube in series with the conduit and having the fluid flowtherethrough, a first sensor operable to determine a first apparentproperty of the fluid flow through the conduit, a second sensorconnected to the flowtube and operable to sense information about amotion of the flowtube, a driver connected to the flowtube and operableto impart energy to the flowtube, a control and measurement systemoperable to measure a second apparent property and a third apparentproperty of the fluid flow, and a corrections system operable todetermine a corrected first property, a corrected second property, and acorrected third property, based on the first apparent property, thesecond apparent property, and the third apparent property.

According to another general aspect, a system includes a controller thatis operable to determine a first apparent property of a fluid flow inwhich a first liquid, a second liquid, and a gas are co-mingled, a meterthat is operable to measure a second apparent property of the fluidflow, and a corrections module that is operable to input the firstapparent property and output a first corrected property, wherein themeter is operable to input the first corrected property and the secondapparent property and output a second corrected property.

The details of one or more implementations are set forth in theaccompanying drawings and the description below. Other features will beapparent from the description and drawings, and from the claims.

DESCRIPTION OF DRAWINGS

FIG. 1A is an illustration of a Coriolis flowmeter using a bentflowtube.

FIG. 1B is an illustration of a Coriolis flowmeter using a straightflowtube.

FIG. 2 is a block diagram of a Coriolis flowmeter.

FIG. 3 is a flowchart illustrating an operation of the Coriolisflowmeter of FIG. 2.

FIG. 4 is a flowchart illustrating techniques for determining liquid andgas flow rates for a two-phase flow.

FIGS. 5A and 5B are graphs illustrating a percent error in a measurementof void fraction and liquid fraction, respectively.

FIG. 6 is a graph illustrating a mass flow error as a function of a dropin density for a flowtube having a particular orientation and over aselected flow range.

FIG. 7 is a flowchart illustrating techniques for correcting densitymeasurements.

FIG. 8 is a table showing a relationship between an apparent densitydrop and an apparent mass flow rate of the two-phase flow.

FIG. 9 is a flowchart illustrating techniques for determining voidfraction measurements.

FIG. 10 is a flowchart illustrating techniques for determining correctedmass flow rate measurements.

FIG. 11 is a table showing a relationship between an apparent mass flowrate and a corrected density drop of the two-phase flow.

FIGS. 12-14 are graphs illustrating examples of density corrections fora number of flowtubes.

FIGS. 15-20 are graphs illustrating examples of mass flow ratecorrections for a number of flowtubes.

FIG. 21 is a block diagram of a flowmeter system.

FIG. 22 is a diagram of a first implementation of the system of FIG. 21.

FIG. 23 is a block diagram of a second implementation of the system ofFIG. 21.

FIG. 24 is a block diagram of an implementation of the correctionssystem 2108 of FIGS. 21-23

FIG. 25 is a flowchart illustrating a first operation of the flowmetersof FIGS. 21-23.

FIG. 26 is a flowchart illustrating a first example of the techniques ofFIG. 25.

FIG. 27 is a flowchart illustrating a second example of the techniquesof FIG. 25.

FIG. 28 is a flowchart illustrating a third example of the techniques ofFIG. 25.

FIG. 29 is a flowchart illustrating techniques for determining componentflow rates for a three-phase flow.

FIG. 30 is a flowchart illustrating more specific techniques forperforming the determinations of FIG. 29.

FIGS. 31A-31D are graphs illustrating correction of a mass flow rate ofa two-phase liquid in a three-phase flow.

FIG. 32 is a graph showing a mass flow error as a function of mass flowrate for oil and water.

FIG. 33 is a graph showing a gas void fraction error as a function oftrue gas void fraction.

FIG. 34 is a graphical representation of a neural network model.

FIG. 35 is a graphical representation of units of the model of FIG. 34.

FIGS. 36A, 36B, and 37A-D illustrate results from two-phase flow data towhich the model of FIGS. 34 and 35 is applied.

FIGS. 38-68 are graphs illustrating test and/or modeling results ofvarious implementations described above with respect to FIGS. 1-37, orrelated implementations.

DETAILED DESCRIPTION

Types of flowmeters include digital flowmeters. For example, U.S. Pat.No. 6,311,136, which is hereby incorporated by reference, discloses theuse of a digital flowmeter and related technology including signalprocessing and measurement techniques. Such digital flowmeters may bevery precise in their measurements, with little or negligible noise, andmay be capable of enabling a wide range of positive and negative gainsat the driver circuitry for driving the conduit. Such digital flowmetersare thus advantageous in a variety of settings. For example,commonly-assigned U.S. Pat. No. 6,505,519, which is incorporated byreference, discloses the use of a wide gain range, and/or the use ofnegative gain, to prevent stalling and to more accurately exercisecontrol of the flowtube, even during difficult conditions such astwo-phase flow (e.g., a flow containing a mixture of liquid and gas).

Although digital flowmeters are specifically discussed below withrespect to, for example, FIGS. 1 and 2, it should be understood thatanalog flowmeters also exist. Although such analog flowmeters may beprone to typical shortcomings of analog circuitry, e.g., low precisionand high noise measurements relative to digital flowmeters, they alsomay be compatible with the various techniques and implementationsdiscussed herein. Thus, in the following discussion, the term“flowmeter” or “meter” is used to refer to any type of device and/orsystem in which a Coriolis flowmeter system uses various control systemsand related elements to measure a mass flow, density, and/or otherparameters of a material(s) moving through a flowtube or other conduit.

FIG. 1A is an illustration of a digital flowmeter using a bent flowtube102. Specifically, the bent flowtube 102 may be used to measure one ormore physical characteristics of, for example, a (traveling) fluid, asreferred to above. In FIG. 1A, a digital transmitter 104 exchangessensor and drive signals with the bent flowtube 102, so as to both sensean oscillation of the bent flowtube 102, and to drive the oscillation ofthe bent flowtube 102 accordingly. By quickly and accurately determiningthe sensor and drive signals, the digital transmitter 104, as referredto above, provides for fast and accurate operation of the bent flowtube102. Examples of the digital transmitter 104 being used with a bentflowtube are provided in, for example, commonly-assigned U.S. Pat. No.6,311,136.

FIG. 1B is an illustration of a digital flowmeter using a straightflowtube 106. More specifically, in FIG. 1B, the straight flowtube 106interacts with the digital transmitter 104. Such a straight flowtubeoperates similarly to the bent flowtube 102 on a conceptual level, andhas various advantages/disadvantages relative to the bent flowtube 102.For example, the straight flowtube 106 may be easier to (completely)fill and empty than the bent flowtube 102, simply due to the geometry ofits construction. In operation, the bent flowtube 102 may operate at afrequency of, for example, 50-110 Hz, while the straight flowtube 106may operate at a frequency of, for example, 300-1,000 Hz. The bentflowtube 102 represents flowtubes having a variety of diameters, and maybe operated in multiple orientations, such as, for example, in avertical or horizontal orientation.

Referring to FIG. 2, a digital mass flowmeter 200 includes the digitaltransmitter 104, one or more motion sensors 205, one or more drivers210, a flowtube 215 (which also may be referred to as a conduit, andwhich may represent either the bent flowtube 102, the straight flowtube106, or some other type of flowtube), and a temperature sensor 220. Thedigital transmitter 104 may be implemented using one or more of, forexample, a processor, a Digital Signal Processor (DSP), afield-programmable gate array (FPGA), an ASIC, other programmable logicor gate arrays, or programmable logic with a processor core. It shouldbe understood that, as described in U.S. Pat. No. 6,311,136, associateddigital-to-analog converters may be included for operation of thedrivers 210, while analog-to-digital converters may be used to convertsensor signals from the sensors 205 for use by the digital transmitter104.

The digital transmitter 104 generates a measurement of, for example,density and/or mass flow of a material flowing through the flowtube 215,based at least on signals received from the motion sensors 205. Thedigital transmitter 104 also controls the drivers 210 to induce motionin the flowtube 215. This motion is sensed by the motion sensors 205.

Density measurements of the material flowing through the flowtube arerelated to, for example, the frequency of the motion of the flowtube 215that is induced in the flowtube 215 by a driving force supplied by thedrivers 210, and/or to the temperature of the flowtube 215.

Similarly, mass flow through the flowtube 215 is related to the phaseand frequency of the motion of the flowtube 215, as well as to thetemperature of the flowtube 215.

The temperature in the flowtube 215, which is measured using thetemperature sensor 220, affects certain properties of the flowtube, suchas its stiffness and dimensions. The digital transmitter 104 maycompensate for these temperature effects. Also in FIG. 2, a pressuresensor 225 is in communication with the transmitter 104, and isconnected to the flowtube 215 so as to be operable to sense a pressureof a material flowing through the flowtube 215.

It should be understood that both the pressure of the fluid entering theflowtube 215 and the pressure drop across relevant points on theflowtube may be indicators of certain flow conditions. Also, whileexternal temperature sensors may be used to measure the fluidtemperature, such sensors may be used in addition to an internalflowmeter sensor designed to measure a representative temperature forflowtube calibrations. Also, some flowtubes use multiple temperaturesensors for the purpose of correcting measurements for an effect ofdifferential temperature between the process fluid and the environment(e.g., a case temperature of a housing of the flowtube). As discussed inmore detail below, one potential use for the inlet fluid temperature andpressure measurements is to calculate the actual densities of a liquidand gas in a two-phase flow, based on predefined formulae.

A liquid fraction probe 230 refers to a device for measuring a volumefraction of liquid, e.g., water, when a liquid in the flowtube 215includes water and another fluid, such as oil. Of course, such a probe,or similar probes, may be used to measure the volume fraction of a fluidother than water, if such a measurement is preferred or if the liquiddoes not include water. In the below description, a measured liquid isgenerally assumed to be water for the purposes of example, so that theliquid fraction probe 230 is generally referred to as a water fractionprobe 230, or a water-cut probe 230.

A void fraction sensor 235 measures a percentage of a material in theflowtube 215 that is in gaseous form. For example, water flowing throughthe flowtube 215 may contain air, perhaps in the form of bubbles. Such acondition, in which the material flowing through the flowtube 215contains more than one material is generally referred to as “two-phaseflow.” In particular, the term “two-phase flow” may refer to a liquidand a gas; however, “two-phase flow” also may refer to othercombinations of materials, such as two liquids (e.g., oil and water).

Various techniques, represented generally in FIG. 2 by the void fractionsensor 235, exist for measuring the gas void fraction in a two-phaseflow of liquid and gas. For example, various sensors or probes existthat may be inserted into the flow to determine a gas void fraction. Asanother example, a venturi tube (i.e., a tube with a constricted throatthat determines fluid pressures and velocities by measurement ofdifferential pressures generated at the throat as a fluid traverses thetube), relying on the fact that gas generally moves with a highervelocity than liquid(s) through a restriction, may be used to determinea pressure gradient and thereby allow a determination of the gas voidfraction. Measurements of gas void fractions also may be obtained usingequipment that is wholly external to the flowtube. For example, sonarmeasurements may be taken to determine gas void fraction. As a specificexample of such a sonar-based system, the SONARtrac™ gas void fractionmonitoring system produced by CiDRA Corporation of Wallingford, Conn.may be used.

In this description, an amount of gas in a flowing fluid, measured bythe void fraction sensor or otherwise determined, is referred to as voidfraction or c, and is defined as α=volume of gas/total volume=volume ofgas/(volume of liquid+volume of gas). Accordingly, a quantity referredto herein as the liquid fraction is defined as 1−α.

In many applications where mass flow measurements are required, the voidfraction of the flow can be as high as 20, 30, 40% or more. However,even at very small void fractions of 0.5%, the fundamental theory behindthe Coriolis flowmeter becomes less applicable.

Moreover, a presence of gas in the fluid flow also may affect both anactual and a measured value of a density of the fluid flow, generallycausing the density measurement to be, and to read, lower than if thefluid flow contained only the liquid component. That is, it should beunderstood that a density ρ_(liquid) of a liquid flowing by itselfthrough a flowtube will be higher than an actual density ρ_(true) of atwo-phase flow containing the liquid and a gas, since a density of thegas (e.g., air) will generally be lower than a density of the liquid(e.g., water) in the two-phase flow. In other words, there is a densityreduction when gas is added to a liquid flow that previously containedonly the liquid.

Beyond this physical phenomenon, a Coriolis meter measuring a two-phasefluid flow containing gas may output a density reading ρ_(apparent) thatis an ostensible measurement of the bulk density of the two-phase flow(e.g., of the water and air combined). This raw measurement ρ_(apparent)will generally be different (lower) than the actual bulk densityρ_(true) of the two-phase flow. For example, the resonant frequency usedby the flowmeter may be correct for a situation in which only the liquidcomponent is present, but, due to relative motion of the gas in thefluid flow, which serves to mask an inertia of the flowtube (i.e.,causes an amount of inertia to be less than would be expected for aliquid-only flow), the density measurement may read low. It should beunderstood that many conventional prior art flowmeters were unconcernedwith this problem, since most such Coriolis meters fail to continueoperating (e.g. stall or output inaccurate measurements) at even theslightest amounts of void fraction.

U.S. Pat. No. 6,505,519, which is incorporated by reference above,discloses that such a variation of ρ_(apparent) (i.e., an indicated bulkdensity reading of a two-phase flow that is output by a Coriolisflowmeter) from ρ_(true) (i.e., an actual bulk density of the two-phaseflow) may be characterized by a variety of techniques. As a result, ameasured ρ_(apparent) may be corrected to obtain an actual bulk densityρ_(corrected), which is, at least approximately, equal to ρ_(true).

Somewhat similarly, an indicated bulk mass flow rate MF_(apparent)(i.e., a mass flow rate of the entire two-phase flow) measured by aCoriolis flowmeter may be different by a predictable or characterizableamount from an actual bulk mass flow rate MF_(true). It should beunderstood that correction techniques for corrected bulk mass flow rateMF_(true) may be different than the techniques for correcting fordensity. For example, various techniques for correcting a measuredMF_(apparent) to obtain an actual MF_(true) (or, at least,MF_(corrected)) are discussed in U.S. Pat. No. 6,505,519.

Examples of detailed techniques for correcting ρ_(apparent) andMF_(apparent) are discussed in more detail below. Generally speaking,though, with respect to FIG. 2, the digital transmitter is shown asincluding a density correction system 240, which has access to a densitycorrection database 245, and a mass flow rate correction system 250,which has access to a mass flow correction database 255. As discussed inmore detail below, the databases 245 and 255 may contain, for example,correction algorithms that have been derived theoretically or obtainedempirically, and/or correction tables that provide corrected density ormass flow values for a given set of input parameters. The databases 245and 255 also may store a variety of other types of information that maybe useful in performing the density or mass flow corrections. Forexample, the density correction database may store a number of densitiesρ_(liquid) corresponding to particular liquids (e.g., water or oil).

Further in FIG. 2, a void fraction determination/correction system 260is operable to determine a void fraction of a two-phase flow including aliquid and a gas. In one implementation, for example, the void fractiondetermination/correction system 260 may determine an actual voidfraction α_(true) from the corrected density ρ_(corrected). In anotherimplementation, the void fraction determination/correction system 260may input an apparent or indicated void fraction measurement obtained bythe void fraction sensor 235, and may correct this measurement based onan error characterization similar to the density and mass flowtechniques referred to above. In another implementation, the voidfraction sensor 235 may be operable to directly measure an actual voidfraction α_(true), in which case the void fractiondetermination/correction system 260 simply inputs this measurement.

Once the factors of ρ_(corrected), MF_(corrected), and α_(corrected)have been determined, and perhaps in conjunction with other known ordiscoverable quantities, a flow component mass flow rate determinationsystem 265 operates to simultaneously determine a mass flow rate for theliquid phase component and a mass flow rate for the gas phase component.That is, the transmitter 104 is operable to determine individualflowrates MF_(liquid) and MF_(gas) of the flow components, as opposed tomerely determining the bulk flowrate of the combined or total two-phaseflow MF_(true). Although, as just referred to, such measurements may bedetermined and/or output simultaneously, they also may be determinedseparately or independently of one another.

Once the component flow rates MF_(liquid) and MF_(gas) have beendetermined in the manner generally outlined above, these initialdeterminations may be improved upon by a process that relies onsuperficial velocities of the flow components, slip velocities betweenthe components, and/or an identified flow regime of the flow. In thisway, improved values for flow rates MF_(liquid) and MF_(gas) may beobtained, or may be obtained over time as those flow rates change.

Superficial velocities are referred to herein as those velocities thatwould exist if the same mass flow rate of a given phase was traveling asa single phase through the flowtube 215. A superficial velocitydetermination/correction system 270 is included in the transmitter 104for, for example, determining an apparent or corrected superficialvelocity of a gas or liquid in the two-phase flow.

Slip velocities refer to a condition in which gas and liquid phases in atwo-phase flow have different average velocities. That is, an averagevelocity of a gas AV_(gas) is different from an average velocity of aliquid AV_(liquid). As such, a phase slip S may be defined asS=AV_(gas)/AV_(liquid).

A flow regime is a term that refers to a characterization of the mannerin which the two phases flow through the flowtube 215 with respect toone another and/or the flowtube 215, and may be expressed, at leastpartially, in terms of the superficial velocities just determined. Forexample, one flow regime is known as the “bubble regime,” in which gasis entrained as bubbles within a liquid. As another example, the “slugregime” refers to a series of liquid “plugs” or “slugs” separated byrelatively large gas pockets. For example, in vertical flow, the gas ina slug flow regime may occupy almost an entire cross-sectional area ofthe flowtube 215, so that the resulting flow alternates betweenhigh-liquid and high-gas composition. Other flow regimes are known toexist and to have certain defined characteristics, including, forexample, the annular flow regime, the dispersed flow regime, and frothflow regime, and others.

The existence of a particular flow regime is known to be influenced by avariety of factors, including, for example, a gas void fraction in thefluid flow, an orientation of the flowtube 215 (e.g., vertical orhorizontal), a diameter of the flowtube 215, the materials includedwithin the two-phase flow, and the velocities (and relative velocities)of the materials within the two phase flow. Depending on these and otherfactors, a particular fluid flow may transition between several flowregimes over a given period of time.

Information about phase slip may be determined at least in part fromflow regime knowledge. For example, in the bubble flow regime, assumingthe bubbles are uniformly distributed, there may be little relativemotion between the phases. Where the bubbles congregate and combine toform a less uniform distribution of the gas phase, some slippage mayoccur between the phases, with the gas tending to cut through the liquidphase.

In FIG. 2, a flow regime determination system 275 is included that hasaccess to a database 280 of flow regime maps. In this way, informationabout an existing flow regime, including phase slip information, may beobtained, stored, and accessed for use in simultaneously determiningliquid and gas mass flow rates within a two-phase flow.

In FIG. 2, it should be understood that the various components of thedigital transmitter 104 are in communication with one another, althoughcommunication links are not explicitly illustrated, for the sake ofclarity. Further, it should be understood that conventional componentsof the digital transmitter 104 are not illustrated in FIG. 2, but areassumed to exist within, or be accessible to, the digital transmitter104. For example, the digital transmitter 104 will typically include(bulk) density and mass flow rate measurement systems, as well as drivecircuitry for driving the driver 210.

FIG. 3 is a flowchart 300 illustrating an operation of the Coriolisflowmeter 200 of FIG. 2. Specifically, FIG. 3 illustrates techniques bywhich the flowmeter 200 of FIG. 2 is operable to simultaneouslydetermine liquid and gas flow rates MF_(liquid) and MF_(gas) for atwo-phase flow.

In FIG. 3, it is determined that a gas/liquid two-phase flow exists inthe flowtube 215 (302). This can be done, for example, by an operatorduring configuration of the mass flowmeter/densitometer for gas/liquidflow. As another example, this determination may be made automaticallyby using a feature of the Coriolis meter to detect that a condition oftwo-phase gas-liquid flow exists. In the latter case, such techniquesare described in greater detail in, for example, U.S. Pat. No. 6,311,136and U.S. Pat. No. 6,505,519, incorporated by reference above.

Once the existence of two-phase flow is established, a corrected bulkdensity ρ_(corrected) is established (304) by the density correctionsystem 240, using the density correction database 245 of the transmitter104. That is, an indicated density ρ_(apparent) is corrected to obtainρ_(corrected). Techniques for performing this correction are discussedin more detail below.

Once ρ_(corrected) is determined, a corrected gas void fractionα_(corrected) may be determined (306) by the void fractiondetermination/correction system 260. Also, a corrected bulk mass flowrate MF_(corrected) is determined (308) by the mass flow rate correctionsystem 250. As with density, techniques for obtaining the corrected voidfraction true and mass flow rate MF_(corrected) are discussed in moredetail below.

In FIG. 3, it should be understood from the flowchart 300 that thedeterminations of ρ_(corrected), α_(corrected), and MF_(corrected) mayoccur in a number of sequences. For example, in one implementation, thecorrected void fraction α_(corrected) is determined based onpreviously-calculated corrected density ρ_(corrected), whereupon thecorrected mass flow rate MF_(corrected) is determined based onα_(corrected). In another implementation, α_(corrected) andρ_(corrected) may be calculated independently of one another, and/orρ_(corrected) and MF_(corrected) may be calculated independently of oneanother.

Once corrected density ρ_(corrected), corrected void fractionα_(corrected), and corrected mass flow rate MR_(corrected) are known,then the mass flow rates of the gas and liquid components are determined(310) by the flow component mass flow rate determination system 265.Techniques for determining the liquid/gas component flow rates arediscussed in more detail below with respect to FIG. 4.

Once determined, the liquid/gas component flow rates may be output ordisplayed (312) for use by an operator of the flowmeter. In this way,the operator is provided, perhaps simultaneously, with information aboutboth the liquid mass flow rate MF_(liquid) and the gas mass flow rateMF_(gas) of a two-phase flow.

In some instances, this determination may be sufficient (314), in whichcase the outputting of the liquid/gas component flow rates completes theprocess flow. However, in other implementations, the determination ofthe individual component mass flow rates may be improved upon byfactoring in information about, for example, the superficial velocitiesof the gas/liquid components, the flow regime(s) of the flow, and phaseslip, if any, between the components.

In particular, superficial velocities of the gas and liquid, SV_(gas)and SV_(liquid) are determined as follows. Gas superficial velocitySV_(gas) is defined as:

SV_(gas)=MF_(gas)/(ρ_(gas) *A _(T))  Eq. 1

where the quantity A_(T) represents a cross-section area of the flowtube215, which may be taken at a point where a void fraction of the flow ismeasured. Similarly, a liquid superficial velocity SV_(liquid) isdefined as:

SV_(liquid)=MF_(liquid)/(ρ_(liquid) *A _(T))  Eq. 2

As shown in Eqs. 1 and 2, determination of superficial velocities inthis context relies on the earlier determination of MF_(gas) andMF_(liquid). It should be understood from the above description and fromFIG. 3 that MF_(gas) and MF_(liquid) represent corrected or true massflow rates, MF_(gas) ^(corrected) and MF_(liquid) ^(corrected) sincethese factors are calculated based on ρ_(true), α_(true), and MF_(true).As a result, the superficial velocities SV_(gas) and SV_(liquid)represent corrected values SV_(gas) ^(corrected) and SV_(liquid)^(corrected). Further, the density values ρ_(gas) and ρ_(liquid) refer,as above, to known densities of the liquid and gas in question, whichmay be stored in the density correction database 245. As discussed inmore detail below with respect to techniques for calculating correcteddensity ρ_(corrected), the density values ρ_(gas) and ρ_(liquid) may beknown as a function of existing temperature or pressure, as detected bytemperature sensor 220 and pressure sensor 225.

Using the superficial velocities and other known or calculated factors,some of which may be stored in the flow regime maps database 280, arelevant flow regime and/or phase slip may be determined (318) by theflow regime determination/correction system 275. Once superficialvelocities, flow regime, and phase slip are known, further correctionsmay be made to the corrected bulk density ρ_(true), corrected bulk massflow rate MF_(corrected), and/or corrected void fraction α_(corrected).In this way, as illustrated in FIG. 3, component flow rates MF_(gas) andMF_(liquid) may be determined.

Flow regime(s) in two phase liquid/gas flow may be described by contourson a graph plotting the liquid superficial velocity versus the gassuperficial velocity. As just described, an improvement todeterminations of ρ_(corrected), α_(corrected), and/or MF_(corrected)may be obtained by first establishing an approximate value of the liquidand gas flow rates, and then applying a more detailed model for the flowregime identified. For example, at relatively low GVF and relativelyhigh flow there exists a flow regime in which the aerated fluid behavesas a homogenous fluid with little or no errors in both density and massflow. This can be detected as homogenous flow requiring no correction,simply using observation of the drive gain, which shows little or noincrease in such a setting, despite a significant drop in observeddensity.

FIG. 4 is a flowchart 400 illustrating techniques for determining liquidand gas flow rates MF_(liquid) and MF_(gas) for a two-phase flow. Thatis, the flowchart 400 generally represents one example of techniques fordetermining liquid and gas flow rates (310), as described above withrespect to FIG. 3.

In FIG. 4, the determination of liquid and gas flow rates (310) beginswith inputting the corrected density, void fraction, and mass flow ratefactors ρ_(corrected), α_(corrected), and MF_(corrected) (402). In afirst instance, (404), the liquid and gas flow rates are determined(406) using Eqs. 3 and 4:

MF_(gas)=α_(corrected)(ρ_(gas)/ρ_(true))(MF_(corrected))  Eq. 3

MF_(liquid)=(1−α_(corrected))(ρ_(liquid)/ρ_(corrected))(MF_(corrected))  Eq.4

Eqs. 3 and 4 assume that there is no slip velocity (i.e., phase slip)between the liquid and gas phases (i.e., average velocity of the gasphase, AV_(gas), and average velocity of the liquid phase, AV_(liquid),are equal). This assumption is consistent with the fact that, in thefirst instance, superficial velocities and flow regimes (and therefore,phase slip) have not been determined.

In the second instance and thereafter (404), a determination is made,perhaps by the flow regime determination/correction system 275, as towhether phase slip exists (408). If not, then Eqs. 3 and 4 are usedagain (406) or the process ends.

If phase slip does exist (408), defined above as S=AV_(gas)/AV_(liquid),the terms MF_(gas) and MF_(liquid) are calculated using thecross-sectional area of the flowtube 215, A_(T), as also used in thecalculation of superficial velocities in Eqs. 1 and 2 (410). Using thedefinition of slip S just given,

MF_(gas)=ρ_(gas)(α_(corrected) A _(T))(AV_(gas))=ρ_(gas)(α_(corrected) A_(T))(S)(AV_(liquid))  Eq. 5

MF_(liquid)=ρ_(liquid)((1−α_(corrected) A _(T))(AV_(liquid))  Eq. 6

Since MF_(corrected)=MF_(gas)+MF_(liquid), Eqs. 5 and 6 may be solvedfor AV_(liquid) to obtain Eq. 7:

AV_(liquid)=MF_(true)/(A_(T)(ρ_(gas)α_(corrected)+ρ_(liquid)(1−α_(corrected))))  Eq. 7

As a result, the liquid and gas flow rates are determined (406) usingEqs. 8 and 9:

MF_(liquid)=[ρ_(liquid)(1−α_(corrected))/(ρ_(gas)α_(corrected)+ρ_(liquid)(1−α_(corrected)))][MF_(corrected)]  Eq.8

MF_(gas)=MF_(corrected)−MF_(liquid)  Eq. 9

As described above, gas entrained in liquid forms a two-phase flow.Measurements of such a two-phase flow with a Coriolis flowmeter resultin indicated parameters ρ_(apparent), α_(apparent), and MF_(apparent)for density, void fraction, and mass flow rate, respectively, of thetwo-phase flow. Due to the nature of the two-phase flow in relation toan operation of the Coriolis flowmeter, these indicated values areincorrect by a predictable factor. As a result, the indicated parametersmay be corrected to obtain actual parameters ρ_(corrected),α_(corrected), and MF_(corrected). In turn, the actual, corrected valuesmay be used to simultaneously determine individual flow rates of the two(gas and liquid) components.

FIGS. 5A and 5B are graphs illustrating a percent error in a measurementof void fraction and liquid fraction, respectively. In FIG. 5A, thepercent error is a density percent error that is dependent on variousdesign and operational parameters, and generally refers to the deviationof the apparent (indicated) density from the true combined density thatwould be expected given the percentage (%) of gas in liquid.

In FIG. 5B, true liquid fraction versus indicated liquid fraction isillustrated. FIG. 5B shows the results, for the relevant flowmeterdesign, of several line sizes and flow rates. In more general terms, thefunctional relationship may be more complex and depend on both line sizeand flowrate. In FIG. 5B, a simple polynomial fit is shown that can beused to correct the apparent liquid fraction.

Other graphing techniques may be used; for example, true void fractionmay be plotted against indicated void fraction. For example, FIG. 6 is agraph illustrating a mass flow error as a function of a drop in densityfor a flowtube having a particular orientation and over a selected flowrange.

FIG. 7 is a flowchart 700 illustrating techniques for correcting densitymeasurements (304 in FIG. 3). In FIG. 7, the process begins with aninputting of the type of flowtube 215 being used (702), which mayinclude, for example, whether the flowtube 215 is bent or straight, aswell as other relevant facts such as a size or orientation of theflowtube 215.

Next, a gas-free density of the liquid, ρ_(liquid) is determined (704).This quantity may be useful in the following calculation(s), as well asin ensuring that other factors that may influence the densitymeasurement ρ_(apparent), such as temperature, are not misinterpreted asvoid fraction effects. In one implementation, the user may enter theliquid density ρ_(liquid) directly, along with a temperature dependenceof the density. In another implementation, known fluids (and theirtemperature dependencies) may be stored in the density correctiondatabase 245, in which case the user may enter a fluid by name. In yetanother implementation, the flowmeter 200 may determine the liquiddensity during a time of single-phase, liquid flow, and store this valuefor future use.

An indicated mass flow rate MF_(apparent) is read from the Coriolismeter (706), and then an indicated density ρ_(apparent) is read from theCoriolis meter (708). Next, the density correction system 240 applieseither a theoretical, algorithmic (710) or empirical, tabular correction(712) to determine the true density ρ_(true) of the gas/liquid mixture.The quantity ρ_(true) may then be output as the corrected density (714).

An algorithmic density correction (710) may be determined based on theknowledge that, if there were no effect of the two-phase flow from thenormal operation of a Coriolis meter when used to measure density, theindicated density would drop by an amount derived from the equationdescribing void fraction, which is set forth above in terms of volumeflow and repeated here in terms of density as Eq. 10:

α_(((%))=[(ρ_(apparent)−ρ_(liquid))/(ρ_(gas)−ρ_(liquid))]×100  Eq. 10

This can be used to define a quantity “density drop,” or Δρ, as shown inEq. 11:

Δρ=(ρ_(liquid)−ρ_(apparent))/ρ_(liquid)=α_((%))×((ρ_(liquid)ρ_(gas))/ρ_(liquid))/100  Eq.11

Note that Eq. 11 shows the quantity Δρ as being positive; however, thisquantity could be shown as a negative drop simply by multiplying theright-hand side of the equation by −1, resulting in Eq. 12:

Δρ=(ρ_(apparent)−ρ_(liquid))/ρ_(liquid)=α_((%))×((ρ_(gas)−ρ_(liquid))/ρ_(liquid))/100  Eq.12

The quantity ρ_(gas) may be small compared to ρ_(liquid), in which caseEq. 12 may be simplified to Eq. 13:

Δρ=(ρ_(liquid)−ρ_(apparent))=α_((%))/100  Eq. 13

As discussed extensively above, density measurements by a Coriolismeter, or any vibrating densitometer, generally are under-reported bythe meter, and require correction. Accordingly, under two-phase flowEqs. 12 or 13 may thus be used to define the following two quantities: acorrected or true density drop, Δρ_(true), and an indicated or apparentdensity drop, A ρ_(app). Using Eq. 13 as one example, this results inEqs. 14 and 15:

Δρ_(true)=(ρ_(liquid)−ρ_(true))=α_((%))/100  Eq. 14

Δρ_(app)=(ρ_(liquid)−ρ_(apparent))=α_((%))/100  Eq. 15

There can be derived or empirically determined a relationship between AΔρ_(true) and Δρ_(apparent) and apparent mass flow rate, MF_(apparent),as well as other parameters, such as, for example, drive gain, sensorbalance, temperature, phase regime, etc. This relationship can beexpressed as shown as Δρ_(true)=f(MF_(apparent), ρ_(apparent), drivegain, sensor balance, temperature, phase regime, and/or other factors).

As a result, the relationship may generally be derived, or at leastproven, for each flowtube in each setting. For one model flowtube, knownand referred to herein as the Foxboro/Invensys CFS10 model flowtube, ithas been empirically determined that for some conditions the abovefunctional relationship can be simplified to be only a function Aρ_(apparent) and of the form shown in Eq. 16:

$\begin{matrix}{{\Delta \; \rho_{true}} = {\sum\limits_{i = 0}^{M}{a_{i}\left( {\Delta \; \rho_{apparent}} \right)}^{i}}} & {{Eq}.\mspace{14mu} 16}\end{matrix}$

To force the condition for both sides of Eq. 16 to be zero when there isno apparent density drop relationship results in Eq. 17:

$\begin{matrix}{{\Delta \; \rho_{true}} = {\sum\limits_{i = 1}^{M}{a_{i}\left( {\Delta \; \rho_{apparent}} \right)}^{i}}} & {{Eq}.\mspace{14mu} 17}\end{matrix}$

M generally depends on the complexity of the empirical relationship, butin many cases can be as small as 2 (quadratic) or 3 (cubic).

Once the true density drop is determined, then working back through theabove equations it is straightforward to derive the true mixture densityρ_(true), as well as the true liquid and gas (void) fractions (thelatter being discussed in more detail with respect to FIG. 9).

A tabular correction for density (712) may be used when, for example, afunctional relationship is too complex or inconvenient to implement. Insuch cases, knowledge of the quantities Δρ_(apparent) and ΔMF_(apparent)may be used to determine Δρ_(true) by employing a table having the formof a table 800 of FIG. 8.

The table 800 may be, for example, a tabular look-up table that can be,for example, stored in the database 245, or in another memory, for useacross multiple applications of the table. Additionally, the table maybe populated during an initialization procedure, for storage in thedatabase 245 for an individual application of the table.

It should be understood that either or both of the algorithmic andtabular forms may be extended to include multiple dimensions, such as,for example, gain, temperature, balance, or flow regime. The algorithmicor tabular correction also may be extended to include other surfacefitting techniques, such as, for example, neural net, radical basisfunctions, wavelet analyses, or principle component analysis.

As a result, it should be understood that such extensions may beimplemented in the context of FIG. 3 during the approach describedtherein. For example, during a first instance, density may be determinedas described above. Then, during a second instance, when a flow regimehas been identified, the density may be further corrected using the flowregime information.

FIG. 9 is a flowchart 900 illustrating techniques for determining voidfraction measurements (306 in FIG. 3). In FIG. 9, the process beginswith an inputting by the void fraction determination system 240 of thepreviously-determined liquid and bulk (corrected) densities, ρ_(liquid)and ρ_(true) (902).

A density of the gas, ρ_(gas) is then determined (904). As with theliquid density ρ_(liquid), there are several techniques for determiningρ_(gas). For example, ρ_(gas) may simply be assumed to be a density ofair, generally at a known pressure, or may be an actual known density ofthe particular gas in question. As another example, this known densityρ_(gas) may be one of the above factors (i.e., known density of air orthe specific gas) at an actual or calculated pressure, as detected bythe pressure sensor 225, and/or at an actual or calculated temperature,as detected by the temperature sensor 220. The temperature and pressuremay be monitored using external equipment, as shown in FIG. 2, includingthe temperature sensor 220 and/or the pressure sensor 225.

Further, the gas may be known to have specific characteristics withrespect to factors including pressure, temperature, or compressibility.These characteristics may be entered along with an identification of thegas, and used in determining the current gas density ρ_(gas). As withthe liquid(s), multiple gasses may be stored in memory, perhaps alongwith the characteristics just described, so that a user may accessdensity characteristics of a particular gas simply by selecting the gasby name from a list.

Once the factors ρ_(liquid), ρ_(gas), and ρ_(true) are known, then itshould be clear from Eq. 10 that void fraction α_(true) may be easilydetermined (906). Then, if needed, liquid fraction may be determined(908) simply by calculating 1−α_(true).

Although the above discussion presents techniques for determining voidfraction α_(true) based on density, it should be understood that voidfraction may be determined by other techniques. For example, anindicated void fraction α_(apparent) may be directly determined by theCoriolis flowmeter, perhaps in conjunction with other void fractiondetermination systems (represented by the void fraction sensor 235 ofFIG. 2), and then corrected based on empirical or derived equations toobtain α_(true). In other implementations, such external void fractiondetermining systems may be used to provide a direct measurement ofα_(true).

FIG. 10 is a flowchart 1000 illustrating techniques for determiningcorrected mass flow rate measurements (308 in FIG. 3). In FIG. 10, themass flow rate correction system 250 first inputs thepreviously-calculated corrected density drop Δρ_(true) (1002), and theninputs a measured, apparent mass flow rate MF_(apparent) (1004).

The mass flow rate correction system 250 applies either a tabular (1006)or algorithmic correction (1008) to determine the true mass flow rateMF_(true) of the gas/liquid mixture. The quantity MF_(true) may then beoutput as the corrected mass flow rate (1010).

In applying the tabular correction for mass flow rate (1006), knowledgeof the quantities Δρ_(true) and ΔMF_(apparent) may be used to determineMF_(true) by employing a table having the form of a table 1100 of FIG.11.

The table 1100, as with the table 800 may be, for example, a tabularlook-up table that can be, for example, stored in the database 245, orin another memory, for use across multiple applications of the table.Additionally, the table may be populated during an initializationprocedure, for storage in the database 255 for an individual applicationof the table.

Normalized values MF_(norm) _(—) _(app) and MF_(norm) _(—) _(true) maybe used in place of the actual ones shown above, in order to cover morethan one size Coriolis flowtube. Also, the entries can be in terms ofthe correction, where the correction is defined by Eq. 18:

ΔMF=MF_(true)−MF_(apparent)  Eq. 18

The values in Eq. 18 should be understood to represent either actual ornormalized values.

In an algorithmic approach, as with density, the correction for massflow may be implemented by way of a theoretical or an empiricalfunctional relationship that is generally understood to be of the formΔMF=f (MF_(apparent), void fraction, drive gain, sensor balance,temperature, phase regime, and/or other factors).

For some cases the function can simplify to a polynomial, such as, forexample, the polynomial shown in Eq. 19:

$\begin{matrix}{{\Delta \; {MF}} = {\sum\limits_{i = 0}^{M}{\sum\limits_{j = 0}^{N}{a_{i}{b_{j}\left( {\Delta \; \rho_{true}^{i}} \right)}\left( {MF}_{norm\_ app}^{j} \right)}}}} & {{Eq}.\mspace{14mu} 19}\end{matrix}$

For some set of conditions, the functional relationship can be acombination of a polynomial and exponential, as shown in Eq. 20:

ΔMF=a ₁ de ^((a) ² ^(d) ² ^(+a) ³ ^(d+a) ⁴ ^(m) ² ^(+a) ⁵ ^(m)) +a ₆ d ²+a ₇ d+a ₈ m ² +a ₉ m  Eq. 20

In Eq. 20, d=Δρ_(true), and m=f(MF_(apparent)).

In one implementation, m in Eq. 20 may be replaced by apparentsuperficial liquid velocity SV_(liquid) which is given as describedabove by Eq. 2 as SV_(liquid)=MF_(liquid)/(ρ_(liquid)*A_(T)). In thiscase, ρ_(liquid) and flowtube cross-section A_(T) are known or enteredparameters, and may be real-time corrected for temperature using, forexample, the on-board temperature measurement device 220 of the digitalcontroller/transmitter 104.

It should be understood that, as with the density corrections discussedabove, either or both of the algorithmic and tabular forms may beextended to include multiple dimensions, such as, for example, gain,temperature, balance, or flow regime. The algorithmic or tabularcorrection also may be extended to include other surface fittingtechniques, such as, for example, neural net, radical basis functions,wavelet analyses, or principle component analysis.

As a result, it should be understood that such extensions may beimplemented in the context of FIG. 3 during the approach describedtherein. For example, during a first instance, mass flow rate may bedetermined as described above. Then, during a second instance, when aflow regime has been identified, the mass flow rate may be furthercorrected using the flow regime information.

All of the above functional relationships for mass flow rate may berestated using gas fraction (α) or liquid fraction (100−α) instead ofdensity drop, as reflected in the table 1100 of FIG. 11. Also, althoughthe above described methods are dependent on knowledge of the correcteddensity drop Δρ_(true), it should be understood that other techniquesmay be used to correct an indicated mass flow rate. For example, varioustechniques for correcting mass flow rate measurements of a two-phaseflow are discussed in U.S. Pat. No. 6,505,519, incorporated by referenceabove.

Having described density, void fraction, and mass flow rate correctionsabove in general terms, for the purpose of, for example, simultaneouslycalculating individual flow component (phases) flow rates in a two-phaseflow, the below discussion and corresponding figures provide specificexamples of implementations of these techniques.

FIGS. 12-14 are graphs illustrating examples of density corrections fora number of flowtubes. In particular, the examples are based on dataobtained from three vertical water flowtubes, the flowtubes being: ½″,¾″, and 1″ in diameter.

More specifically, the ½″ data was taken with a 0.15 kg/s flow rate anda 0.30 kg/s flow rate; the ¾″ data was taken with a 0.50 kg/s flow rateand a 1.00 kg/s flow rate; and the 1″ data was taken with a 0.50 kg/sflow rate, a 0.90 kg/s flow rate, and a 1.20 kg/s flow rate. FIG. 12illustrates an error, e_(d), of the apparent density of the fluid-gasmixture (two-phase flow) versus the true drop in density of thefluid-gas mixture, Δρ_(true):

$\begin{matrix}{{\Delta\rho}_{true} = {100 \cdot \frac{\rho_{liquid} - \rho_{true}}{\rho_{liquid}}}} & {{Eq}.\mspace{14mu} 21} \\{e_{d} = {100 \cdot \frac{\rho_{apparent} - \rho_{true}}{\rho_{true}}}} & {{Eq}.\mspace{14mu} 22}\end{matrix}$

where, as above, ρ_(liquid) is the density of the gas-free liquid,ρ_(true) is the true density of the liquid-gas mixture, and ρ_(apparent)is the apparent or indicated density of the liquid-gas mixture.

In FIGS. 12-14, the correction is performed in terms of the apparentdrop in mixture density, Δρ_(apparent), as shown in Eq. 23:

$\begin{matrix}{{\Delta\rho}_{apparent} = {100 \cdot \frac{\rho_{liquid} - \rho_{apparent}}{\rho_{liquid}}}} & {{Eq}.\mspace{14mu} 23}\end{matrix}$

In FIGS. 12-14, when fitting the data, both the apparent and true dropin density of the mixture were normalized to values between 0 and 1 bydividing them through by 100, where this normalization is designed toensure numerical stability of the optimization algorithm. In otherwords, the normalized apparent and true drop in mixture density are theapparent and true drop in mixture density defined as a ratio, ratherthan as a percentage, of the liquid density ρ_(liquid), as shown in Eq.24:

$\begin{matrix}{{\Delta\rho}_{apparent}^{normalized} = \frac{{\Delta\rho}_{apparent}}{100}} & {{Eq}.\mspace{14mu} 24}\end{matrix}$

The model formula, based on Eq. 17, provides Eq. 25:

Δρ_(true) ^(normalized) =a ₁(Δρ_(apparent) ^(normalized))³ +a₂(Δρ_(apparent) ^(normalized))² +a ₃(Δρ_(apparent) ^(normalized))  Eq.25

In this case, the coefficients are a₁=−0.51097664273685,a₂=1.26939674868129, and a₃=0.24072693119420. FIGS. 13A and 13Billustrate the model with the experimental data and the residual errors,as shown. FIGS. 14A and 14B give the same information, but with eachflow rate plotted separately.

To summarize, the drop in density correction is performed in thetransmitter 104 by calculating the apparent density drop Δρ_(apparent),using the apparent density value ρ_(apparent) and the liquid densityρ_(liquid). The value of the apparent drop in density is normalized toobtain

${{\Delta\rho}_{apparent}^{normalized} = \frac{{\Delta\rho}_{apparent}}{100}},$

so that, as explained above, the drop in density is calculated as aratio rather than a percentage. The density correction model(s) may thenbe applied to obtain the normalized corrected drop in mixture densityΔρ_(true) ^(normalized). Finally, this value is un-normalized to obtainthe corrected drop in density Δρ_(true)=100·Δρ_(true) ^(normalized). Ofcourse, the final calculation is not necessary if the corrected drop inmixture density Δρ_(true) is defined as a ratio rather than percentageof the true value.

FIGS. 15-20 are graphs illustrating examples of mass flow ratecorrections for a number of flowtubes. In particular, the examples arebased on data obtained from three vertical water flowtubes, theflowtubes being: ½″, ¾″, and 1″ in diameter. More specifically, the ½″data was taken with a 0.15 kg/s flow rate and a 0.30 kg/s flow rate; the¾″ data was taken with a 0.50 kg/s flow rate and a 1.00 kg/s flow rate;and the 1″ data was taken with 18 flow rates between 0.30 kg/s and 3.0kg/s flow rate, with a maximum drop in density of approximately 30%.

FIGS. 15A and 15B illustrate apparent mass flow errors for the data usedto fit the model versus corrected drop in mixture density Δρ_(true) andnormalized true superficial fluid velocity; i.e., the apparent mass flowerror curves per flowline, together with a scatter plot of the apparentmass flow error versus corrected drop in density Δρ_(true) andnormalized true superficial fluid velocity v_(m), as shown in Eq. 26:

$\begin{matrix}{{v_{tn} = \frac{v_{t}}{v_{\max}}},{v_{t} = \frac{m_{t}}{\rho_{liquid} \cdot A_{T}}}} & {{Eq}.\mspace{14mu} 26}\end{matrix}$

where m_(t) is the true fluid mass flow, i.e. the value of the mass flowindependently measured, ρ_(liquid) is the liquid density, A_(T) is theflowtube cross-section area, and v_(max) is the maximum value for thesuperficial fluid velocity (here considered 12 m/s), so that v_(tn)gives the ratio of the true superficial fluid velocity from the wholerange of the flowtube 215. In these examples, both drop in mixturedensity and superficial fluid velocity are normalized between 0 and 1prior to fitting the model, for the purpose of ensuring numericalstability for the model optimization algorithm.

FIG. 16 illustrates apparent mass flow errors versus corrected drop inmixture density and normalized apparent superficial fluid velocity, withsafety bounds for the correction mode. That is, FIG. 16 gives thescatter plot of the apparent mass flow errors versus corrected drop indensity and, this time, normalized apparent superficial fluid velocity

${v_{n} = {\frac{v}{v_{\max}} = \frac{m}{v_{\max} \cdot \rho \cdot A}}},$

where m is the apparent fluid mass flow (i.e. as measured by thetransmitter 104). Superimposed on the plot are the boundaries definingthe safe region for the model, i.e., the region for which the model isexpected to give an accuracy similar with the one for the fit data.Using this nomenclature, the apparent mass flow error e is given by

$e = {100 \cdot {\frac{m - m_{t}}{m_{t}}.}}$

The model formula for this situation is shown as Eq. 27:

e _(n) =a ₁ dd _(cn) ·e ^(a) ² ^(dd) ^(cn) ² ^(+a) ³ ^(dd) ^(cn) ^(+a) ⁴^(v) ^(n) ² ^(+a) ⁵ ^(v) ^(n) +a ₆ dd _(cn) ² +a ₇ dd _(cn) +a ₈ v _(n)² +a ₉ v _(n)  27

where

$\begin{matrix}{e_{n} = {\frac{e}{100} = \frac{m - m_{t}}{m_{t}}}} & {{Eq}.\mspace{14mu} 28}\end{matrix}$

where, in Eqs. 27 and 28, dd_(cn) is the normalized corrected drop inmixture density, and v_(n) is the normalized apparent superficialvelocity of the liquid.

In this case, the coefficient are: a₁=−4.78998578570465,a₂=4.20395000016874, a₃=−5.93683498873342, a₄=12.03484566235777,a₅=−7.70049487145105, a₆=0.69537907794202, a₇=−0.52153213037389,a₈=0.36423791515369, and a₉=−0.16674339233364

FIG. 17 illustrates a scatter plot for the model residuals, togetherwith the model formula and coefficients; i.e., shows model residualsversus the corrected drop in mixture density and normalized true fluidvelocity. FIGS. 18A-18D and FIGS. 19A-19D give the model residual errorsfor the whole data set used to fit the model and the actual data alone,respectively. Finally, FIGS. 20A and 20B illustrate the model surfaceboth interpolating and extrapolating outside the safe fit area. FromFIGS. 16, 20A, and 20B, the apparent mass flow (superficial liquidvelocity) and drop in density bounds for the model should be understood.

To summarize, mass flow correction in the transmitter 104 is undertakenin this example by calculating an apparent drop in density, correctingit using the method(s) described above, and normalizing the resultingvalue by dividing it by 100 (or use the obtained normalized correcteddrop in density from the density model). Then, a normalized superficialfluid velocity v, is calculated, and the model is applied to obtain anestimation of the normalized mass flow error e_(n), where this valuegives the error of the apparent mass flow as a ratio of the true massflow. The obtained value may be un-normalized by multiplying it by 100,to thereby obtain the mass flow error as a percentage of the true massflow. Finally, the apparent mass flow may be corrected with theun-normalized mass flow error

$m_{c} = {\frac{m}{e_{n} + 1}.}$

As will be appreciated, the above description has a wide range ofapplications to improve the measurement and correction accuracy of aCoriolis meter during two phase flow conditions. In particular, thetechniques described above are particularly useful in measurementapplications where the mass flow of the liquid phase and the mass flowof the gas phase must be measured and/or corrected to a high level ofaccuracy. One exemplary application is the measurement of the mass flowof the liquid phase and the measurement of the gas phase in oil and gasproduction environments.

The above discussion is provided in the context of the digital flowmeterof FIG. 2. However, it should be understood that any vibrating oroscillating densitometer or flowmeter, analog or digital, that iscapable of measuring multi-phase flow that includes a gas phase of acertain percentage may be used. That is, some flowmeters are onlycapable of measuring process fluids that include a gas phase when thatgas phase is limited to a small percentage of the overall process fluid,such as, for example, less than 5%. Other flowmeters, such as thedigital flowmeter(s) referenced above, are capable of operation evenwhen the gas void fraction reaches 40% or more.

Many of the above-given equations and calculations are described interms of density, mass flow rate, and/or void fraction. However, itshould be understood that the same or similar results may be reachedusing variations of these parameters. For example, instead of mass flow,a volumetric flow may be used. Additionally, instead of void fraction,liquid fraction may be used.

The above discussion provides examples of measuring component mass flowrates in a two-phase flow. Flowmeters also may be used to measurefurther mixed flows. For example, a “three-phase” flow or “mixedtwo-phase flow” refers to a situation in which two types of liquid aremixed with a gas. For example, a flowing mixture of oil and water maycontain air (or another gas), thus forming a “three-phase flow,” wherethe terminology refers to the three components of the flow, and does notgenerally imply that a solid material is included in the flow.

FIG. 21 is a block diagram of a flowmeter system 2100. The flowmetersystem 2100 may be used, for example, to determine individual componentflow rates within a three-phase flow. For example, the system 2100 maybe used to determine an amount of oil within an oil, water, and gas flowthat travels through a pipe at an oil extraction facility, during agiven period of time.

The flowmeter system 2100 also may be used to obtain highly-accuratemeasurements from the digital transmitter 104, such as, for example,density measurements or mass flow rate measurements. The system 2100also may be used, for example, to obtain an improved measurement from anexternal sensor, such as, for example, the liquid fraction probe 230, orthe void fraction sensor 235, relative to what measurements might beobtained using the external sensor(s) alone.

In FIG. 21, the digital transmitter 104 includes a void fractiondetermination system 2102, a density determination system 2104, and amass flow rate determination system 2106 (in addition to a number ofcomponents that are not shown for clarity's sake, e.g., a drive signalgenerator, or a multi-phase detection system, or any of the componentsillustrated or discussed with respect to FIG. 2). That is, as should beunderstood from the above description, the systems 2102, 2104, and 2106may be used to measure corresponding parameters of a fluid flow withinthe flow 215. Further, as also explained above, to the extent that thefluid flow contains gas and/or mixed liquids, the measurements output bythe systems 2102, 2104, and 2106 generally represent raw or apparentvalues for the corresponding parameters, which ultimately may becorrected with a corrections system 2108.

For example, an apparent mass flow rate of a three-phase fluid flowwithin the flowtube 215 may be output to the corrections system 2108 forcorrection using a mass flow rate correction module 2112, while anapparent density of the three-phase fluid flow within the flowtube 215may be output to the corrections system 2108 for correction using adensity correction module 2118. Somewhat similarly, a measurement ordetermination of an apparent void fraction within the fluid flow may becorrected using a density correction module 2114, while a measurement ordetermination of an apparent liquid fraction (e.g., water cut from probe230) may be corrected using a water cut correction module 2116. Asdescribed in more detail below, the various correction modules 2112-2118may work in conjunction with one another, and/or with other components,in order to obtain their respective corrected values.

Once obtained, corrected values such as mass flow rate, density, watercut, or void fraction (or some combination thereof) may be output to ahost computer 2110 for determination of individual mass flow rates ofeach of the three components of the three-phase fluid flow, using acomponent flow rate determination system 2120. As a result, and asreferenced above, individual flow rates and/or amounts of each of thethree components may be determined.

More generally, an example of the system 2100 includes three generalelements used to obtain corrected measurement values and/or individualcomponent flow rates: the transmitter 104, one or more of the individualexternal sensors identified generically with a reference numeral 2122,and one or more elements of the corrections system 2108. Of course, manycombinations, variations, and implementations of these elements may beused, various examples of which are discussed in more detail below.

For example, in some implementations, the digital transmitter 104 maynot include the void fraction determination system 2102. In some cases,the void fraction determination system 2102 may be included with, orassociated with, the liquid fraction probe 230, or may be unneededdepending on a type or configuration of the void fraction sensor 235. Insuch cases, to the extent that it is needed, the void fraction may bedetermined from outputs of the correction modules 2112, 2116, and/or2118.

Further, although the external sensors 2122 are shown in FIG. 21 to bein communication with the digital transmitter 104 and the flowtube 215,it should be understood that the external sensors 2122 may obtain theirrespective measurements in a number of different ways. For example,examples of the temperature sensor 220, the pressure sensor 225, and thevoid fraction sensor 230 are described above, with respect to, forexample, FIG. 2. Further, the liquid fraction probe 235 may be in serieswith the flowtube 215 with respect to a primary pipe for transportingthe three-phase fluid flow, and may maintain separate communication withthe transmitter 104, the corrections system 2108, and/or the hostcomputer 2110.

In FIG. 21, the corrections system 2108 is shown as being separate fromthe digital transmitter 104 and the host computer 2110. In someimplementations, however, the corrections system 2108 may be locatedwithin the digital transmitter 104, the host computer 2110, or may beassociated with one or more of the external sensors 2122. In still otherimplementations, portions of the corrections system 2108 may be includedwithin different sections of the system 2100. For example, density andmass flow rate corrections may be performed at the digital transmitter104, while water cut corrections may be performed at the liquid fractionprobe 230.

In some implementations, the corrections system 2108 may include all ofthe modules 2112-2118 (as shown), or some subset thereof, or may includeother modules, not specifically illustrated in FIG. 21 (e.g., acorrections module for correcting a density of the two-liquid componentwithin the three-phase flow, such as the oil/water mixture in anoil/water/gas fluid flow). Further, some or all of any such correctionmodules may be integrated with one another.

For example, the mass flow rate and density corrections may beincorporated into one module, while the water cut correction module 2116may be separate.

Along the same lines, it should be understood that the component flowrate determination system 2120 may be situated in a number of placeswithin the system 2100. For example, the component flow ratedetermination system 2120 may be located within the corrections system2108, or may be located within the digital transmitter 104.

Various examples of the above and other implementations, as well asexamples of specific techniques for obtaining corrected flowmeasurements and individual component flow rates, are described in moredetail below. In general, however, it should be understood that thesystem 2100 and other implementations thereof allows for all orsubstantially all of the three-phase fluid flow to flow continuouslythrough the flowtube 215 and through an associated pipe or other conduitfor transporting the three-phase flow material.

As a result, determinations of individual component flow rates do notrequire separation of the three-phase fluid flow into separate flowscontaining one or more of the constituent components. For example, whenthe three-phase flow contains oil, water, and gas, it is not necessaryto separate the gas from the oil/water liquid combination in order toperform measurements (e.g., mass flow rate) on the oil portion of theresulting oil/liquid flow. Accordingly, reliable measurements of anamount of oil produced, for example, at an oil production facility, maybe made easily, quickly, inexpensively, and reliably.

FIG. 22 is a diagram of a first implementation of the system 2100 ofFIG. 21. In FIG. 22, the liquid fraction probe 230 is illustrated as awater cut probe that is in series with the digital transmitter 104 withrespect to three-phase fluid flow through a pipe 2202. Examples of usingmeasurements from the water cut probe 230 in determining flowmeasurements are provided in more detail below.

Also in FIG. 22, a static mixer-sampler 2204 is illustrated that servesto homogenize the three-phase fluid. The mixer-sampler 2204 also may beused for other measurements. For example, the mixer-sampler 2204 may beused to validate measurements of the water cut probe 230, or othermeasurements. In one implementation, the mixer-sampler 2204 may be usedto siphon off a portion of a three-phase flow of oil/water/gas forevaporation of the gas therefrom, for independent confirmation of awater fraction within the resulting two-liquid composition.

Somewhat similarly, a pressure transmitter 2206 may be used in variouspost-processing techniques for validating or confirming measurements ofthe system.

FIG. 23 is a block diagram of a second implementation of the system ofFIG. 21. In FIG. 23, the liquid fraction probe 230 is illustrated as amicrowave water-cut probe 230 a and/or an infrared water-cut probe 230b. A power supply 2302 for supplying power to the system also isillustrated. The flowtube 215 of FIG. 23 should be understood tocontain, for example, the bent flowtube 102 of FIG. 1A, although, ofcourse, the straight flowtube 106 of FIG. 1B, or some other flowtube,also may be used.

Further in FIG. 23, the sensors 230 a, 230 b, and/or 2206 areillustrated as being in bi-directional communication with thetransmitter 104, including a standard 4-20 mA control signal.

Meanwhile, the transmitter 104 is in communication with the hostcomputer 2110 by way of a Modbus RS485 connection.

Also, as referenced above, FIG. 23 illustrates several possiblelocations for the corrections system 2108. For example, as shown, thecorrections system 2108 may be located at, or associated with, aprocessor associated with the host computer 2110, or with the digitaltransmitter 104, and/or with the water-cut probe 230 a (and/or otherexternal sensor 230 b).

FIG. 24 is a block diagram of an implementation of the correctionssystem 2108 of FIGS. 21-23. In FIG. 24, and as should be apparent fromthe above description of FIG. 21, the corrections system 2108 inputs,from the transmitter 104, measurements such as an apparent (or raw)measurement of a liquid fraction (e.g., water cut) of the three-phaseflow, along with an apparent bulk mass flow rate and apparent bulkdensity.

The corrections system 2108 in this example includes a water cut errormodel 2402 and a Coriolis error model 2404. The models 2402 and 2404, asshown, allow for calculations of the corrected, or the estimation of thetrue, corresponding measurements of water cut, mass flow rate, anddensity. In other words, as should be apparent from the above discussionof two-phase fluid flows, 2402 and 2404 model known configurations andflow parameters, so that subsequently measured flow parameters may becorrelated with the modeling results by way of, for example,interpolation.

For example, as discussed in more detail below, the models 2402 and 2404may be implemented to provide polynomial fittings of measured (apparent)flow parameters. In other examples, the models 2402 and 2404 mayrepresent neural net correction models for correcting water cut and massflow/density.

In the example of FIG. 24, where the available measurement includes anapparent water cut, then the resulting corrected measurements allow forthe calculation of the additional parameter of gas void fraction.Conversely, if an apparent gas void fraction were available, rather thanan apparent water cut measurement, then the corrections system mayoutput a corrected void fraction measurement (thereby allowingsubsequent estimation of a true water cut). In either case, or insimilar cases, the corrections system 2108 may output the correctedmeasurements to the component flow rate determination system 2120 forcalculation of individual component mass flow rates.

FIG. 24 illustrates an example in which the outputs of each model 2402and 2404 are fed back into one another, in order to obtain sequentiallybetter results, before outputting a final value for corrected water cut,(bulk) mass flow rate, and (bulk) density, and, thereafter, calculatingindividual component flows. In other words, for example, it is assumedthat the initial determination of an apparent water cut may be dependenton, and vary with, an amount of gas within the three-phase fluid flow(i.e., the gas void fraction). However, an accurate value of the gasvoid fraction may not generally be available until after an estimate ofthe true water cut measurement has been determined.

Therefore, as illustrated, by feeding the values of a firstdetermination of a corrected water cut value from the water cut errormodel 2402 back into the Coriolis error model 2404, an improved estimateof corrected mass flow rate, density, and gas void fraction may beobtained, and, thereafter, fed back into the water cut error model. Thisprocess may continue, for example, until a desired level of accuracy isreached, or until a determined amount of time has passed.

In FIG. 24, the models 2402 and 2404 may be orthogonal to one another,so that one may be replaced without affecting an operation of the other.For example, if a new water cut probe is used (e.g., the probe 230 ainstead of the probe 230 b of FIG. 23), then a corresponding water cuterror model may similarly be substituted, while the Coriolis error modelmay continue to be used.

In other implementations, and, for example, where a specific water cutprobe, Coriolis meter, and configuration thereof with respect to oneanother are known and assumed to be unchanging, then it may be possibleto construct a single error model that inputs all three measurements ofwater cut, mass flow rate, and density, and outputs corrected values ofall three (along with, possibly, a corrected gas void fraction). In suchimplementations, it may not be necessary to feed sequential results backinto the error model in order to obtain all three (or four, or more)corrected values.

FIG. 25 is a flowchart 2500 illustrating a first operation of theflowmeter of FIGS. 21-23.

More particularly, FIG. 25 represents a high-level description of manydifferent techniques and combinations of techniques, specific examplesof some of which (along with other examples) are presented in moredetail, below.

In FIG. 25, existence of a three-phase flow is determined and apparentmeasurements are obtained (2502). For example, the transmitter 104 mayobtain an apparent bulk density and an apparent mass flow rate, and theliquid fraction probe 230 may obtain an apparent water cut measurement.As shown in FIG. 21, these measurements may then be output to thecorrections system 2108.

In this way, a corrected water cut (2504), corrected bulk density(2506), corrected bulk mass flow rate (2508), and corrected gas voidfraction (2510), may be obtained. As illustrated, there are manyvariations for obtaining these corrected measurements.

For example, the corrected mass flow rate may be determined based onlyon apparent measurements, such as apparent mass flow rate, or may bedetermined based on these factors along with an already-correcteddensity and/or gas void fraction measurement. Similar comments apply,for example, to techniques for obtaining corrected density and/or gasvoid fraction measurements. Also, it should be apparent that otherfactors and parameters may be used in calculating corrected values thatare not necessarily shown in FIG. 25, such as, for example, temperature,pressure, liquid or gas densities of the flow components, or otherparameters, known or measured.

Further, as referenced above, a given correction may be obtainedmultiple times, with later corrections being based on interveningcorrections of other parameters. For example, a first-corrected watercut measurement may be obtained, and may then be revised based on afollowing void fraction determination, to obtain a second-correctedwater cut measurement.

Once some or all of the corrected parameters are obtained, individualcomponent flow rates for one or more of the first liquid component,second liquid component, and gas component may be obtained (2512). Then,these outputs, and/or the corrected values themselves, may be displayedor otherwise output (2514).

FIG. 26 is a flowchart 2600 illustrating a first example of thetechniques of FIG. 25. In particular, in FIGS. 21-25, correcting bulkdensity may be associated with determining a water cut measurement,using the water cut probe 230.

Thus, in FIG. 26, an existence of a three-phase flow having a firstliquid, a second liquid, and a gas is assumed, and the process beginswith a determination of an apparent water cut measurement (2602). Then,the density of the mixture of the two liquids is determined (2604).

Based on this knowledge, an apparent gas void fraction α_(apparent) isdetermined (2606). Then, in one implementation, the process 2600continues with a determination of corrected values of, for example, bulkdensity and bulk mass flow rate (2608).

Once these values are known, a correction for gas void fractionα_(corrected) may be performed (2610), resulting in a new, reviseddetermination of gas void fraction (2606). In this way, a correction ofthe initial water cut measurement may be performed (2612), so as to takeinto account an effect of the gas within the three-phase flow on theinitial water cut measurement (2602), and thereby obtain an improvedwater cut measurement.

Then, the improved water cut measurement may be used to determine andimprove the liquid density measurement (2604), which, in turn, may beused to determine a corrected or improved gas void fraction measurement(2606). As a result, further-corrected bulk density and bulk mass flowrate measurements may be obtained (2608).

The process 2600, or variations thereof, may be continued untilsatisfactory results for corrected values of bulk density, bulk massflow rate, water cut, and/or gas void fraction have been determined.Then, individual mass flow rates for the three components (e.g., oil,water, and gas) of the multiphase flow may be determined.

Specific equations and discussion for implementing the example processes2500 and 2600, as well as for subsequent examples, are provided below.In this context, specific examples of how and why selected parametersare used also are provided.

For example, water cut in a two-phase flow is defined as the volumefraction of water in the two-phase (e.g., oil-water) mixture, whendevoid of gas. Under this condition, water cut is given by Eq. 29:

$\begin{matrix}{{WC} = \frac{\rho_{liquid} - \rho_{oil}}{\rho_{w} - \rho_{oil}}} & {{Eq}.\mspace{14mu} 29}\end{matrix}$

where ρ_(liquid) is the oil-water mixture density, ρ_(oil) and ρ_(w) arethe pure oil and pure water densities, respectively. Of course, theliquid components of oil and water are just examples, and other liquidsmay be used.

Generally, in the case of just a two-phase oil-water flow, where no gasis present, the Coriolis flowmeter may measure the mixture (bulk)density, ρ_(liquid), and the mixture mass flow rate, MF. The water cutof the mixture is then calculated based on Eq. 29. This technique isdescribed in more detail in, for example, U.S. Pat. No. 5,029,482,assigned to Chevron Research Company, and may be useful in derivingwater cut from a density measurement using a Coriolis flowmeter.

The volumetric flow rate of the liquid (oil-water) mixture may bederived using Eq. 30:

$\begin{matrix}{{VF}_{liquid} = \frac{{MF}_{liquid}}{\rho_{liquid}}} & {{Eq}.\mspace{14mu} 30}\end{matrix}$

Thus, the two independent measurements of bulk (mixture) density andmass flow rate by the Coriolis flowmeter provide sufficient informationto satisfy the mathematical closure requirement where two components arepresent in the combined stream.

Eqs. 29 and 30, however, cannot be directly applied when three distinctphases (i.e., oil, water and gas) are in a co-mingled stream, i.e., athree-phase flow, as discussed above with respect to FIGS. 21-25,because the Coriolis flowmeter may measure the density and massflow ofthe mixture of the two liquids and gas. In the three-phase case of, forexample, oil-water-gas flow, a third component is introduced whichbenefits from a third independent source of information to satisfymathematical closure for three-phase flow.

In the implementations described above, the independent information isprovided by another device installed in-line with the Coriolisflowmeter, which encounters the same three-phase mixture, i.e., thewater cut probe 230. The water cut probe 230, as described above withrespect to FIGS. 21-25, may be of any possible technologies includingmicrowave, capacitance, capacitance-inductance, nuclear magneticresonance, infrared, and near infrared, and may be implemented using acombination of these types of water cut probes. The use of other typesof water cut probes (or, more generally, liquid fraction probes) isenvisioned within the scope of the present description, as well.

The transmitter 104, as described above, may be used to provide anapparent bulk density, ρ_(apparent) as well as an apparent bulk massflow rate, MF_(apparent). Meanwhile, in this example, the water cutprobe 230 may be used to obtain an apparent water cut measurementWC_(apparent). The density of the oil-water liquid portion only of thethree-phase mixture may thus be derived from the water cut informationas shown in Eq. 31, where, as above, component liquid densities areknown or may be obtained, for example, according to techniques that alsoare described above.

ρ_(liquid)=−(1−WC_(apparent))ρ_(OIL)+WC_(appaennt) ¹⁰ρ_(w)  Eq. 31

The gas void fraction, α, as referenced above, is defined as the volumefraction occupied by the gas phase in the three-phase mixture. Adefinition of α in terms of apparent or non-corrected values, isprovided above and repeated here as Eq. 32:

$\begin{matrix}{\alpha_{apparent} = \frac{\rho_{apparent} - \rho_{liquid}}{\rho_{gas} - \rho_{liquid}}} & {{Eq}.\mspace{14mu} 32}\end{matrix}$

The density of the gas phase in Eq. 32 above may be calculated based onan independent measurement of process pressure and temperature. Forexample, pressure may be measured with the pressure transmitter 225,while the temperature is either measured independently using atemperature transmitter or obtained from the Coriolis flowmeter'stemperature, e.g., the temperature sensor 220, such as a ResistanceTemperature Detector (RTD). Application of, for example, American GasAssociation (AGA) algorithms, incorporated into the transmitter 104, maythen be used to provide the gas phase density.

In Eq. 32, and as already described with respect to FIG. 26, thecalculated liquid phase density (2604) and gas void fraction (2606)based on the water cut input are approximations, since the water cutmeasurement itself is affected by the presence of gas, which heretoforeis unknown. A solution technique to converge to the correct liquid phasedensity and gas void fraction may thus be used, as shown in FIG. 26.

Specifically, following application of mass flow and bulk densitycorrections, an updated gas void fraction is obtained (2610, 2606). Thisupdated gas void fraction value is then applied to the water cut readingto correct for the effect of the presence of gas (2612, 2602).

For each specific water cut device, the relationship between water cutand the effect of gas void fraction may be known as shown in Eq. 33:

WC_(apparent)=ƒ(α_(apparent),ρ_(apparent),MF_(apparent),others)  Eq. 33

That is, an apparent water cut measurement may be a function of manydifferent parameters, so that a corrected water cut measurementWC_(corrected) may generally be a function of the same parameters,corrected values of those parameters, and/or of the apparent water cutmeasurement itself.

With the water cut reading updated, the process is repeated, startingwith Eq. 31, until suitable convergence criteria has been satisfied.Then, the corrected three-phase mixture (bulk) mass flow rate, density,and gas void fraction may be reported at process temperature.

The individual volumetric flow rate of each phase/component is thencalculated and corrected to standard temperature using, for example, theAmerican Petroleum Institute (API) equations for crude oil and producedwater, and the AGA algorithms for produced gas. These functionalitiesalso may be incorporated into the transmitter 104.

For example, in one implementation, the water cut meter 230 may beoperable to feed its measurement signal and information directly intoeither an analog or digital communications port (input/output) of thetransmitter 104. In another implementation, the water cut meter iscapable of communicating with the transmitter 104 in a bi-directionalcommunications mode. As part of this implementation, the water cut meteris able to feed its measured signal and information directly into thecommunications port of the transmitter 104 as just described. Thetransmitter 104 also may be capable of sending signals and informationto the water cut probe 230.

FIG. 27 is a flowchart 2700 illustrating a second example of thetechniques of FIG. 25. In FIG. 27, as in FIG. 26, the process 2700begins with a determination of an apparent water cut measurement (2702).

Then, the water cut measurement may be used to determine a density ofthe total liquid component (e.g., a density of a combined oil and waterportion of the three-phase flow), perhaps using Eq. 31 (2704). Anapparent bulk density of the multiphase flow, or an apparent densitydrop as described above, may be determined (2706), and an apparent gasvoid fraction may be determined, either independently of, or based on,the apparent bulk density (2708). Similarly, an apparent mass flow rateof the total liquid component may then be calculated (2710), using someor all of the previously-calculated parameters.

At this point, first values for corrected and bulk density and correctedbulk mass flow rate may be determined (2712). Then, values for acorrected gas void fraction (2714), a corrected total liquid componentmass flow rate (2716), and a revised or corrected water cut measurement(2718) may be determined.

With the revised water cut measurement and other parameters, a revisedgas void fraction measurement may be obtained. Then, as shown, furthercorrections to the bulk mass flow rates and bulk density may beperformed, and this process may be repeated until a suitable level ofcorrection is reached. And, as described above with respect to FIGS. 25and 26, outputs for the corrected bulk mass flow rate, corrected bulkdensity, corrected water cut measurement, and/or corrected gas voidfraction measurements may be obtained. Also, although not explicitlyillustrated in FIG. 27, mass flow rates for the three individualcomponents of the multiphase flow may be obtained.

FIG. 28 is a flowchart 2800 illustrating a third example of thetechniques of FIG. 25. The process of FIG. 28 begins, as in the process2700, with determinations of water cut measurements, total liquiddensity, and apparent bulk density (2702, 2704, 2706). Then, an apparentbulk mass flow rate is determined (2802).

Based on this information, corrected values for bulk density and bulkmass flow rate may be determined (2804). Then, a gas density may bedetermined, as, for example, a function of pressure and temperature(2806). Accordingly, a gas void fraction can be determined (2808) andcorrected (2810). Using the corrected gas void fraction, a revised watercut measurement can be determined (2812), and used to calculate animproved liquid density, and the process repeated until a satisfactoryresult is reached.

As with FIG. 26, and in combination with the discussion thereof,specific examples, equations, and techniques are presented below forimplementing the processes of FIGS. 27 and 28. Of course, othertechniques also may be used.

The water cut probe 230 or other instrument, as described above,provides a measurement of the volumetric ratio of water to bulk liquidin the liquid phase, as shown in Eq. 34 (2702), where the water cutvalue WC initially represents an apparent water cut value (i.e.,calculated based on apparent values of mass flow and density) that maybe improved or corrected as the processes continue, as alreadydescribed:

$\begin{matrix}{{WC} = {\frac{{VF}_{w}}{{VF}_{w} + {VF}_{oil}} = \frac{\frac{{MF}_{w}}{\rho_{w}}}{\frac{{MF}_{w}}{\rho_{w}} + \frac{{MF}_{oil}}{\rho_{oil}}}}} & {{Eq}.\mspace{14mu} 34}\end{matrix}$

The flowmeter is therefore able to use the water cut measurement tocalculate the liquid phase density as shown in Eq. 31 (2704). From thisthe flowmeter is able to determine the apparent drop in density causedby the presence of the gas, as discussed above with respect to, forexample, a normalized Eq. 23, which is reproduced here for convenience:

$\begin{matrix}{{\Delta\rho}_{apparent} = \frac{\rho_{liquid} - \rho_{apparent}}{\rho_{liquid}}} & {{Eq}.\mspace{14mu} 23}\end{matrix}$

and, as described above, apply a correction algorithm, according to theorientation of the meter, apply a cubic form of Eq. 17, also reproducedhere for convenience:

$\begin{matrix}{{\Delta\rho}_{true} = {\sum\limits_{i = 1}^{M}{a_{i}\left( {\Delta\rho}_{apparent} \right)}^{i}}} & {{Eq}.\mspace{14mu} 17}\end{matrix}$

and determine a corrected mixture density using Eq. 35:

ρ_(true)=(1−Δρ_(true))ρ_(liquid)  Eq. 35

which can be used to calculate a ‘best estimate’ of the gas voidfraction defined by Eq. 32, above.

Other techniques for use with the processes of FIGS. 25-28 should beunderstood from the above discussion of similar calculations in thecontext of, for example, two-phase (e.g., liquid and gas) flow. Inparticular, it should be understood that some or all of the equationsused in a two-phase setting may be applicable with respect to athree-phase flow, inasmuch as a three-phase flow of, for example, oil,water, and gas, may be considered to be a two-phase flow of gas with andoil/water mixture. Still other techniques for using the systems of FIGS.21-24 are described below with respect to data gathered with respect tospecific uses and implementations thereof.

FIG. 29 is a flowchart 2900 illustrating techniques for determiningcomponent flow rates for a three-phase flow. That is, FIG. 29corresponds to a more detailed view of determining component flow rates,as shown in FIG. 25 (2512).

In FIG. 29, the parameters of corrected bulk mass flow rate, correctedbulk density, and corrected gas void fraction (and/or corrected watercut) are input (2902). Then, a corrected liquid flow rate is determined(2904), i.e., a flow rate of the mixture of the two liquids (e.g., oiland water) in the three-phase flow.

A mass flow rate of a first liquid component (e.g., water) is thendetermined (2906), followed by a determination of a mass flow rate ofthe second liquid component (e.g., oil) (2908). Finally, the correcteddensity, gas void fraction, and/or water cut value may be used todetermine a mass flow rate of the gas component of the three-phase flow(2910).

FIG. 30 is a flowchart 3000 illustrating examples of more specifictechniques for performing the determinations of FIG. 29. In FIG. 30, itshould be understood that the corrected mass flow rates of the liquidand its components are determined independently of the corrected densityor gas void fraction measurements.

Specifically, an apparent gas void fraction is determined (3002), usingEq. 32, above.

Then, an apparent gas flow rate is determined (3004), using Eq. 36:

$\begin{matrix}\begin{matrix}{{M\; F_{apparent}^{gas}} = {{\alpha_{apparent}\left( \frac{\rho_{gas}}{\rho_{apparent}} \right)}M\; F_{apparent}}} \\{= {\left( \frac{\rho_{gas}}{\rho_{liquid} - \rho_{gas}} \right)\left( \frac{\rho_{liquid} - \rho_{apparent}}{\rho_{apparent}} \right)M\; F_{apparent}}}\end{matrix} & {{Eq}.\mspace{14mu} 36}\end{matrix}$

Then, an apparent superficial gas velocity is determined (3006). Theapparent superficial gas velocity may be calculated by the volumeflowrate of the liquid divided by the flowtube cross sectional area A,as shown above, and reproduced here, in Eq. 1:

$\begin{matrix}{{S\; V^{gas}} = \frac{M\; F^{gas}}{\rho_{gas}A_{\tau}}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$

An apparent liquid flow rate may then be determined (3008). The apparentliquid phase mass flowrate may be derived from the apparent bulk massflowrate and apparent gas void fraction, using Eq. 37:

$\begin{matrix}\begin{matrix}{{M\; F_{apparent}^{liquid}} = {{M\; F_{apparent}} - {M\; F_{apparent}^{gas}}}} \\{= {\left( {1 - \alpha_{apparent}} \right)\left( \frac{\rho_{liquid}}{\rho_{apparent}} \right)M\; F_{apparent}}}\end{matrix} & {{Eq}.\mspace{14mu} 37}\end{matrix}$

Apparent superficial liquid velocity can then be determined (3010). Tofind the apparent superficial liquid velocity, the volume flowrate ofthe liquid may be divided by the flowtube cross sectional area A_(T), asshown above and reproduced here in Eq. 2:

$\begin{matrix}{{S\; V^{liquid}} = \frac{M\; F^{liquid}}{\rho_{gas}A_{\tau}}} & {{Eq}.\mspace{14mu} 2}\end{matrix}$

Then, an error rate for liquid mass flow measurement is determined(3012). This error in the apparent liquid mass flowrate may be definedas a fraction of the true liquid mass flow, as shown in Eq. 38:

$\begin{matrix}{{{error}\left( {MF}_{apparent}^{liquid} \right)} = \left\lbrack \frac{{M\; F_{apparent}^{liquid}} - {M\; F_{true}^{liquid}}}{M\; F_{true}^{liquid}} \right\rbrack} & {{Eq}.\mspace{14mu} 38}\end{matrix}$

This fractional liquid mass flow error as a function of both apparentsuperficial liquid and apparent superficial gas flows (normalized) maybe estimated using a polynomial expression shown in Eq. 39, where theerror term is shown as e_(l) ^(c) to indicate a corrected error for theliquid mass flow:

$\begin{matrix}{\mspace{79mu} {{{v_{\ln}^{a} = \frac{v_{l}^{a}}{v_{l\; \max}}},\mspace{20mu} {v_{gn}^{a} = \frac{v_{g}^{a}}{v_{g\; \max}}}}{e_{l}^{c} = {{a_{1}{v_{gn}^{a} \cdot e^{{a_{2}v_{gn}^{a\; 2}} + {a_{3}v_{gn}^{a}} + {a_{4}v_{\ln}^{a\; 2}} + {a_{5}v_{lm}^{a}}}}} + {a_{6}v_{gn}^{a\; 2}} + {a_{7}v_{gn}^{a}} + {a_{8}v_{\ln}^{a\; 2}} + {a_{9}v_{\ln}^{a}}}}}} & {{Eq}.\mspace{14mu} 39}\end{matrix}$

In Eq. 39, due to the size of the expression(s), the following notationis used: v_(ln) ^(a) refers to a normalized apparent liquid flow(replacing “l” with “g” in the subscript for the corresponding gasparameter), where normalization is based on, for example, a maximumpossible flowrate(s), as indicated by v_(lmax) and v_(gmax).

A corrected liquid mass flow rate measurement may be determined (3014),using Eqs. 38 and 39, expressed here as Eq. 40:

$\begin{matrix}{{M\; F_{corrected}^{liquid}} = \left\lbrack \frac{M\; F_{apparent}^{liquid}}{1 + {{error}\left( {M\; F_{apparent}^{liquid}} \right)}} \right\rbrack} & {{Eq}.\mspace{14mu} 40}\end{matrix}$

Then, the water cut and component densities may be determined (3016), orobtained using the above-described techniques, and used to determine acorrected oil flow rate and a corrected water flow rate (3018). Then,using the corrected bulk density and corrected gas void fraction (3020),a corrected gas flow rate may be determined (3022).

For example, the water and oil mass flowrates may be calculated, usingEqs. 41 and 42:

$\begin{matrix}{{M\; F_{corrected}^{water}} = {W\; {C_{corrected}\left( \frac{\rho_{water}}{\rho_{corrected}^{liquid}} \right)}M\; F_{corrected}^{liquid}}} & {{Eq}.\mspace{14mu} 41} \\{{M\; F_{corrected}^{oil}} = {\left( {1 - {W\; C_{corrected}}} \right)\left( \frac{\rho_{oil}}{\rho_{corrected}^{liquid}} \right)M\; F_{corrected}^{liquid}}} & {{Eq}.\mspace{14mu} 42}\end{matrix}$

Then, using the corrected mixture density (or corrected gas voidfraction), the gas mass flowrate may be determined using Eqs. 43 and 44:

$\begin{matrix}\begin{matrix}{{M\; F_{corrected}^{gas}} = {{\alpha_{corrected}\left( \frac{\rho_{gas}}{\rho_{corrected}} \right)}M\; F_{corrected}}} \\{= {{\left( \frac{\alpha_{corrected}}{1 - \alpha_{corrected}} \right)\left( \frac{\rho_{gas}}{\rho_{corrected}^{liquid}} \right)M\; F_{corrected}^{liquid}} =}} \\{= {\left( \frac{\rho_{gas}}{\rho_{corrected}^{liquid}} \right)\left( \frac{\rho_{corrected}^{liquid} - \rho_{corrected}}{\rho_{corrected} - \rho_{gas}} \right)M\; F_{corrected}^{liquid}}}\end{matrix} & {{Eq}.\mspace{14mu} 43} \\\begin{matrix}{{M\; F_{corrected}^{gas}} = {{\alpha_{corrected}\left( \frac{\rho_{gas}}{\rho_{corrected}} \right)}M\; F_{corrected}}} \\{= {{\left( \frac{\alpha_{corrected}}{1 - \alpha_{corrected}} \right)\left( \frac{\rho_{gas}}{\rho_{corrected}^{liquid}} \right)M\; F_{corrected}^{liquid}} =}} \\{= {\left( \frac{\rho_{gas}}{\rho_{corrected}^{liquid}} \right)\left( \frac{\rho_{corrected}^{liquid} - \rho_{corrected}}{\rho_{corrected} - \rho_{gas}} \right)M\; F_{corrected}^{liquid}}}\end{matrix} & {{Eq}.\mspace{14mu} 44}\end{matrix}$

It should be understood that, based on the single phase densities andtheir variation with temperature, it is possible to convert the massflows to volume flows at a reference temperature.

In some cases, there may be uncertainty in the polynomial fit to theerror curves, where the effect of this uncertainty on the corrected massflowrate is given by Eq. 45:

$\begin{matrix}{{C\; E} = {\frac{\left( {{M\; F_{corrected}^{liquid}} - {M\; F_{true}^{liquid}}} \right)}{M\; F_{true}^{liquid}} = \frac{\left( {e_{apparent}^{liquid} - e_{true}^{liquid}} \right)}{\left( {1 + e_{true}^{liquid}} \right)}}} & {{Eq}.\mspace{14mu} 45}\end{matrix}$

Eq. 45 helps to explain why some data may exhibit large errors when thecorrection algorithms are use outside a tested region. For example, ifthe calculated error at a given flowrate is −70%, but the true error is−75% then the model error is only 5%, but the error in the correctedmass flow is

$\frac{{- 0.7} + 0.75}{1 - 0.75} = {0.2 = {20\%}}$

Such a calculation also may be used in 2-phase flow modeling results asdescribed above, to consider resulting residual error in the modeling.In one implementation, the model least square fit may be modified tominimize the resultant mass flow error rather than the model error.Also, generally speaking, a flowtube may be expected to exhibit smallmass flow errors, so that if a flowmeter is expected to correct forlarge errors, then the error modeling (and hence experimental data)becomes relatively more important.

Thus, as described above with respect to FIG. 30, apparent superficialvelocities are used to carry out mass flow corrections, so as todecouple the bulk density correction from the liquid mass flowcorrection.

FIGS. 31A-31D are graphs illustrating correction of a mass flow rate ofa two-phase liquid in a three-phase flow. FIGS. 31A-31D show thepredicted liquid mass flow errors when the 3-phase flow correctionalgorithm is applied to data obtained from four oil+water+gas trialsusing a vertical orientation. FIGS. 31A-31D show that the basiccorrection curve does work within 5% for all but the highest gas flows,which are outside the range of data used for modeling.

FIG. 32 is a graph showing a mass flow error as a function of mass flowrate for oil and water. FIG. 33 is a graph showing a gas void fractionerror as a function of true gas void fraction. FIGS. 32 and 33illustrate the errors in estimating the three mass flow fractions byspreadsheet implementation of the above algorithms.

It should be noted that the actual determination of the gas mass flowmay be affected by uncertainty in the mixture density and a relativedifference in density between the liquid and gas phase. Also, it shouldbe understood that the density correction polynomial discussed above maybe more or less applicable depending on, for example, flowtubeorientation. As a result, for example, horizontal flow may result in alower error than vertical flow, or vice-versa.

In the above-described approach, the use of superficial liquid and gasvelocities may enable the correction algorithms to include knowledge ofthe multi-phase flow regimes encountered, which may lead to bettercorrection algorithms.

The results on practical data indicate that the correction polynomialcurves may benefit from being designed on data spanning the expectedflow-ranges, and from being ‘jacketted’ to prevent spurious results whenexposed to data outside the known range.

Although the implementations discussed above make use of an externalwater cut probe or similar technique, other implementations could beused that rely on the external void fraction sensor/meter 235, and/or onother input parameters.

Additionally, as referenced above, other devices, such as those designedto determine an “oil-cut,” rather than a water cut, may be used.Further, if oil and water in a mixture have well-separated densities, asampling system may be used that takes a representative sample of themixture, de-gasses it and uses a Coriolis meter to determine the watercut.

As described, in the case of single liquid two-phase flow, knowledge ofthe liquid and gas densities at the operation temperature and pressuremay be used with the corrected density and massflow measurements tocalculate each of the liquid and gas mass flow rates, and, thereby, theliquid and gas volumetric flow.

In the case of three-phase flow, extra, external measurements may beused to enable the estimation of gas mass flow and the mass flow of eachof the two liquids. In the case of water and oil liquid mixture, thewater cut of the mixture may be measured up-stream of the Coriolismeter, as explained and illustrated above. In one implementation, it maybe assumed that the two liquids do not interact in such a way as toinvalidate the assumption that the mixture of the two liquid behave as asingle liquid as far as the interaction with the gas phase is concerned.This assumption makes the three-phase flow an extension of thesingle-liquid two-phase flow, the extra measurements being used todetermine the mixed liquid density and to decouple the separate liquidmassflows, after two-phase flow calculations are applied.

As further discussed above, a Coriolis meter will generally under-readboth the mixture density and the mixture massflow of a liquid/gasmixture. To compensate for the errors in these raw measurements andestimate the true measurement values, a model for the error surfaces maybe used so as to find a mapping between the raw density and massflowmeasurements, and the value of the raw measurement errors, for bothmassflow and density measurements, i.e., to perform a data fitting.

As already pointed out, both the density and massflow error curve maydepend on many factors, such as, for example, meter size, meterorientation (e.g., horizontal vs. vertical), and a nominal liquid massflow. Accordingly, corrections may be developed for each individualmeter size and orientation. In other implementations, the compensationsmay be scaled according to meter size and/or adjusted according to meteralignment.

General data fitting techniques include, for example, table lookup,polynomial/rational function interpolation, non-linear methods, andneural networks, among others. For example, FIG. 24 illustrates errormodels that may be implemented using neural networks.

FIG. 34 shows a particular form of neural network model, the multi layerperceptron (MLP), with just two layers of weights 3412, 3414 andsigmoidal hidden units 3408, has been demonstrated to be capable ofapproximating any continuous mapping function to arbitrary accuracy(provided that the number of hidden units is sufficiently large), alsoreferred to as the universality property. This is intuitively supportedby the idea that any reasonable functional mapping can be approximatedwith arbitrary accuracy by a linear superposition (performed by theoutput units activation functions) of a sufficiently large number ofnon-linear functions (represented by the hidden units activationfunctions). Moreover, being a feed-forward network (i.e. there are nointernal loops in data streaming from inputs to outputs), its outputsare deterministic functions of the inputs, making the whole networkequivalent to a multivariate non-linear functional mapping.

For the design of a flexible compensation technique for two- orthree-phase flow errors in a Coriolis meter, neural network modelspresent at least the following advantageous features. For example, suchmodels provide the ability to derive a non-linear functional mappingfrom a sufficiently large and representative database of relevantmeasurements, without prior knowledge of the underlying physical modelof the process. Such a feature may be particularly advantageous in theexample of the two/three-phase flow compensation problem, where actualphysical processes inside the tube may be difficult to obtain.

Further, development time for a viable solution for a particular problemmay be significantly reduced compared with other data fittingtechniques, which may rely on domain expertise. For example, in theparticular case of two-phase flow compensation, changing metersize/orientation/type might completely change the shape of the rawmeasurements surface, and for a conventional data technique, this mayimply a process of finding another form for the functional mapping thatis not guaranteed to find a solution in a reasonable time. By contrast,using the same neural network architecture, the neural network trainingmay find the “best” (in the sense of the cost function chosen to controlthe network training) solution for the data available by adjusting itsinternal parameters during the training process.

The following discussion provides explanation of one example of a neuralnetwork, i.e., an MLP model. Specifically, FIG. 34 is a graphicalrepresentation of the MLP model.

To model raw measurements error surfaces for density and mass flow, asdiscussed above, a functional mapping may be given by MeasError=F(dd,{dot over (m)}), with dd the apparent drop in mixture density and {dotover (m)} the apparent massflow of the liquid. It should be noted thatthis notation is slightly different from the above notation for the sameparameters, i.e., Δp and MF, respectively.

FIG. 34 thus illustrates a multi-layer perceptron (MLP) model with twoinputs (dd 3402 and {dot over (m)} 3404) and one output (MeasError3406). The behavior of each unit is graphically represented in FIG. 35.

An output y 3510 of a unit may be given by applying an activationfunction ƒ 3502 to the weighted sums 3504 of the n unit inputs x_(i)3506, to thus define a unit function 3508, as shown in FIG. 35 and inEq. 46:

$\begin{matrix}{y = {f\left( {\sum\limits_{i = 1}^{n}{w_{i}x_{i}}} \right)}} & {{Eq}.\mspace{14mu} 46}\end{matrix}$

In general terms, an MLP is a feed-forward neural network architecturewith several layers of units. Being feed-forward means that the dataflows monotonically from inputs to outputs, without inner loops; thisensures that the outputs function is deterministic. In order to ensurethe universality property, the MLP used for two-phase flow measurementerror compensation may be a two-layer architecture with sigmoidalactivation functions for hidden units 3308 and linear activationfunction for the output unit 3410.

In this case, the sigmoidal activation function may be given by

${{{sig}(a)} = \frac{1}{1 + ^{- a}}},$

while the linear activation function may be represented as lin(a)=a.

Then, an output of the MLP used as a function of the inputs can bewritten as in Eq. 47:

$\begin{matrix}\begin{matrix}{{MeasError} = {\sum\limits_{i = 1}^{nh}{w_{i}^{output}{{sig}\left( {{w_{i}^{input}{dd}} + {w_{2}^{input}\overset{.}{m}}} \right)}}}} \\{= {\sum\limits_{i = 1}^{nh}{w_{i}^{output}\frac{1}{1 + ^{- {({{w_{1}^{input}{dd}} + {w_{2}^{input}\overset{.}{m}}})}}}}}}\end{matrix} & {{Eq}.\mspace{14mu} 47}\end{matrix}$

That is, Eq. 47 represents a non-linear function in apparent drop inmixture density and massflow, with nh the number of hidden units 3408.

The network parameters w^(input), w^(output) and nh may be determinedduring a process called network training, essentially, an optimizationof a cost function. As stated above, to ensure the universalityproperty, nh has to be sufficiently large (it actually dictates thedegree of freedom for the model, hence its complexity). However, itsvalue should be chosen appropriately; a value too small may lead to apoor fit to the training data, while too large a value may lead to poorgeneralisation capabilities due to over-fitting the training data (theparallel in the field of conventional polynomial data fitting is thedegree of the polynomial).

There are various methods for choosing the number of hidden units 3408.One technique is to perform an exhaustive search for nh (within somereasonable limits) and choose the value for which the bestgeneralization is achieved.

The general outline of one implementation of a training process isdescribed below. The data available for the training is divided intothree independent sets: the training set (used to iteratively change thevalues of the MLP weights to minimize the cost function); the validationset (used to stop the training early to avoid over-fitting the trainingdata); and the test set (used to choose the number of hidden units).

In one implementation, the network training starts with an initial setof network weights w₀=(w^(input) ⁰ , w^(output) ⁰ ) and successivelychanges them to minimize a pre-defined cost function, e.g., the meansquare error. At each such change, the outputs of the MLP correspondingto the data in the training set may be evaluated, and the values of theweights are updated according to a specific “learning rule,” as known inthe field of neural network design, in order to minimize the costfunction value over the training set.

The cost function also may be evaluated over the validation set, and thetraining stopped when this starts increasing, so that a suitablecompromise between the fit of the training data and the generalizationcapabilities may be achieved. That is, over-fitting from training toconvergence over the training set may be avoided. If enough data isavailable, a test set also may be used to assess the performance ofseveral MLP trained, as described, but with different numbers of hiddenunits to choose the architecture that gives the minimum cost functionover the test set.

In the case of massflow compensation, for a low GVF region, thecompensation accuracy may be increased if this area is consideredseparate from the rest and modeled accordingly. Such approach(es)suggest the use of a “committee of models,” also referred to as a“mixture of experts,” with separate but overlapping areas of expertiseto enable soft switching between the models.

An example of such a committee, one used to compensate the raw massflowerrors for a 1″ flowtube in vertical alignment, is:

Model 1: 0-1.5.kg/s, 0-15% GVF

Model 2: 0-1.5 kg/s, 10% GVF upwards

Model 3: 1.2 kg/s upwards, 0-15% GVF

Model 4: 1.2 kg/s upwards, 10% GVF upwards

A different model, referred to as a “blanket model,” also may be trainedusing the whole range of flows and GVFs. The blanket network may be usedto provide a rough idea about the true liquid massflow. Using thisestimation together with the estimated true GVF (based on the densitycompensation model), a specific expert model (or a combination of twoexpert models if the data falls in the overlap region) may be selected,and its compensation applied.

FIGS. 36A, 36B, and 37A-D illustrate results from two-phase flow datacollected for a 1″ Coriolis flowmeter, in both horizontal and verticalalignment, with water and air. Fifty-five flowlines were used, withnominal flow ranging from 0.35 kg/s to 3.0 kg/s in steps of 0.025 kg/s,with typical GVF steps of 0.5% and 1% GVF (depending on the nominal flowvalue), giving a total of 3400 experimental points, for an average of 45points per flowline. The corresponding surfaces for raw density andmassflow errors are given in FIGS. 36A and 36B, respectively.

Based on this data, compensation solutions for density and liquidmassflow errors as described above may be derived and validated online,using independent test data, as shown in FIGS. 37A-37D. The model inputsfor the compensation technique are the raw normalised liquid superficialvelocity

$v_{\ln}^{a} = {\frac{v_{l}^{a}}{v_{l\; \max}} = \frac{\frac{M\; F_{apparent}^{liquid}}{A_{\tau}\rho_{liquid}}}{v_{l\; \max}}}$

(with notation in which A_(τ) represents a cross-sectional area of theflowtube and v_(lmax) the maximum superficial velocity of the liquid,and MF_(apparent) ^(liquid) a mass flow rate of the liquid) and theapparent drop in mixture density.

The test data in this example included thirteen flowlines, with nominalflows ranging from 0.6 kg/s to 3 kg/s, in steps of 0.25 kg/s, with GVFsteps of 2%, giving a total of 266 experimental points, an average of 20points per flowline.

FIGS. 38-68 are graphs illustrating test and/or modeling results ofvarious implementations described above with respect to FIGS. 1-37, orrelated implementations. More specifically, FIGS. 38-68, unless statedotherwise below, are graphs reflecting results from three-phase trialsin which the fluids used were crude oil with a 35° API gravity,simulated brine (i.e., salt-water mixture) with 2% by weight NaCl, andnitrogen. The tests were conducted at a pressure of approximately 150psig and temperature of 100° F.

In the following description and figures, reference is made to thefollowing test conditions:

Test00wc—4000 bpd

Test00wc—6000 bpd

Test06wc—3000 bpd

Test06wc—4000 bpd

Test06wc—6000 bpd

Test06wc—8000 bpd

Test13wc—3000 bpd

Test13wc—6000 bpd

Test25wc—3000 bpd

Test25wc—7000 bpd

Test35wc—3000 bpd

Test35wc—7000 bpd

Test50wc—3000 bpd

Test50wc—5000 bpd

Test50wc—7000 bpd

Test50wc—8000 bpd

In this context, FIGS. 38A and 38B illustrate gas-induced errorresulting from the raw density and mass flow measurements, respectively,of the Coriolis meter.

FIG. 39 illustrates the observed response of the water cut probe used inthese trials. For this particular device, the presence of free gasreduces the observed water cut compared to the true value (for thegas-free oil-water mixture), decreasing monotonically as gas voidincreases.

The response also may be a function of the total mass rate and theintrinsic water cut of the liquid phase, among other factors. For agiven gas void fraction (GVF) level, the observed water cut generallydecreases as total mass rate and intrinsic water cut increases. Thewater cut response surface also may be affected by parameters such as,for example, fluid properties and flow regime.

FIGS. 40A-40C illustrate residual errors for a bulk mixture mass flowand density, and water cut measurements, after a neural-net basedmodeling has been completed, based on the data sets shown in FIGS. 38A,38B, and 39, with water cuts ranging from 0 to 50%. The bulk mass flowerrors are mostly kept within 2% of reading, the bulk density errors aremostly within 1% of reading, and the water cut errors are mostly within2% of the 0-100% fullscale range.

FIG. 41 illustrates how these results are mapped into the correspondingvolumetric flow errors for the oil, water, and gas streams. Note thatfor both the gas and water volumes, low absolute volumetric flow (forwater at low water cuts, and gas at low GVFs) may lead to largepercentage errors as a proportion of the reading. As the oil flow ratemay be significant in these trials, the errors in percentage termsremain mostly within 5%

FIGS. 42-47 are graphs demonstrating techniques for extending mass flowcalculations to generate volumetric oil, water and gas readings. FIGS.42-47 also demonstrate how errors in water cut reading may impact on theoil, water and gas volumetric measurements.

In FIGS. 42-47, massflow and density error corrections are based on theabove-described oil data, with 6% water-cut and a reference water cutvalue of 5.5%. Since the graphs themselves also are based on this dataset, the mass flow and density error predictions are relatively small,which is not necessarily pertinent to the demonstration of how water cutaccuracy affects volumetric measurements.

The Coriolis principle and relate techniques, as described above,provide estimates for an overall mass flow and density of thethree-phase, mixed fluid. Knowledge of the true fluid densities and(perhaps estimated or corrected) water cut, together with models oftwo-phase flow errors, gives estimates of the fluid-only mass flow rate,and the gas void fraction (GVF). Thus, in FIGS. 42-47, finalcalculations are illustrated, in which, given the fluid-only mass flowrate and the water cut, the volumetric flowrates of the oil and gascomponents are obtained, while the GVF yields the gas volumetricflowrate.

Accordingly, FIGS. 42-44 illustrate the calculations of volumetricwater, oil, and gas flow rates, respectively, assuming the water cut isknown perfectly. Under this assumption, both oil and water volumetricerrors are consistently small, being primarily dependent upon theresidual modeling errors for the density and mass flow corrections,which, under the conditions, are small.

The gas volumetric flow may be sensitive to errors in the densitycalculation at low GVFs. For example, with 2% GVF, a 1% absolute errorin the estimate of GVF may lead to 50% error in the estimated volumetricgas flow. Such large relative errors may generally be associated withrelatively low gas flows, and, therefore, may be unlikely to besignificant in oil and gas applications, such as the examples describedherein.

FIGS. 45-47 illustrate the same calculations when the water cut estimateis in error by +1% absolute. This is a reasonable margin of error,allowing for basic measurement accuracy, followed by corrections for theeffects of two or three-phase flow.

More specifically, FIG. 45 illustrates the water volumetric error with a+1% water cut absolute error. The large mean error is about 16%. With atrue water cut of only 6% of the total liquid volume, an error of 1%absolute in the water cut estimate may result in approximately 16%over-estimate of the water volumetric flowrate.

FIG. 46 illustrates that corresponding errors for oil volumetric floware much smaller, reflecting the smaller impact the 1% water cut errorhas on the 94% oil cut measurement.

Finally, FIG. 47 illustrates the impact of the water cut error on thegas volume measurement.

Thus, gas flow errors may be seen to be sensitive to water cut errors atlow GVF, where this influence may decrease with higher GVFs.

FIGS. 49-50 are graphs illustrating a correction of reading from awater-cut meter (i.e., the Phase Dynamics water cut meter) forgas-induced errors. The data for FIGS. 48-50 is based on the oil datadescribed above, with nominal water-cut values of 0.0, 5.5, 13.1, 24.8,35.6 and 50.0%. Although an actual water cut output is cutoff isgenerally zero, raw frequency data and characteristic equationsassociated with operations of the water cut meter allow for extendedwater cut readings which fall below zero %, as shown.

In this context, the water-cut meter has an error even at 0% GVF, due tothe presence of residual amounts of gas ‘carry-under’ from the process,as follows (in absolute water-cut units) with respect to the specifiedtest results referred to above:

Test00wc—4000 bpd: −0.52

Test00wc—6000 bpd: −1.91

Test06wc—3000 bpd: −0.89

Test06wc—4000 bpd: −0.74

Test06wc—6000 bpd: −1.53

Test06wc—8000 bpd: −2.78

Test13wc—3000 bpd: 1.17

Test13wc—6000 bpd: 0.87

Test25wc—3000 bpd: 0.91

Test25wc—7000 bpd: −0.56

Test35wc—3000 bpd: 0.74

Test35wc—7000 bpd: −0.35

Test50wc—3000 bpd: 3.89

Test50wc—5000 bpd: 2.64

Test50wc—7000 bpd: 2.90

Test50wc—8000 bpd: 2.31

For the purpose of correcting the gas-induced errors, the water-cutmeter was considered without error at 0% GVF (as in FIG. 1).

In FIGS. 48 and 49, a neural net, along the lines described above, wasbuilt with inputs of: raw water cut reading, true mass flow reading, andtrue void fraction. The outputs include water cut error (in absoluteunits of water cut—in this case percentage). Accordingly, successivecalculations between this neural network and mass flow/densitycorrections, as described above, lead to a converged overall solution.

With the data as described, the water-cut meter reading may be correctedfrom errors as large as—40% to mainly within 2 percent absolute error,as shown in FIG. 48, which, as referenced above with respect to FIGS.42-47, may impact the water and oil corrections for the Coriolis meter.

FIG. 48 appears to illustrate that the neural network model fails tocorrect properly for some lines, but a detailed study of the lines inquestion shows that the model is a smooth, least-square approximation ofthe experimental behavior, while the actual water-cut error data is morenon-linear (for examples, see FIG. 49). As with the density and massflow errors, higher data density (i.e. more experimental points) mayprovide improvement in the quality of the fit, and also may allow for agood assessment of the level of experimental noise.

FIG. 50-54 are graphs illustrating successive correction of liquids andgas massflow and using the water-cut correction, as generally describedabove with respect to FIG. 27. In FIGS. 50-54, data is based on the oildata as described above, with nominal water-cut value of 5.5%, whilemassflow and density corrections used at this stage are based on oildata with 6% water-cut. The water cut correction model (i.e., neuralnetwork model) used here is the one described above with respect toFIGS. 48 and 49.

Raw water-cut errors are described and shown above with respect to FIG.39, which shows the raw water-cut error, as described above, however,for the rest of the flow analysis, the water-cut reading is limitedwithin 0 and 100%, with values outside the range being forced to takethe limit value.

FIGS. 50A and 50B illustrate raw mixture density and massflow errors,respectively. FIGS. 51A-51C illustrate raw errors for the water, oil,and gas massflows, respectively. FIG. 52 illustrates convergence aftertwo repetitions of FIG. 27, with the water-cut measurement correctedwithin 3%, the mixture density mainly within 1% and massflow mainlywithin 2%.

FIGS. 53A-53C illustrate the corrected water-cut behavior during theprocess. Water, oil, and gas correction accuracies are illustrated inFIGS. 54A-54C, respectively. Here, the oil massflow is corrected towithin 3%. In FIGS. 54A-54C, the water massflow is most affected, with2-3% error in water-cut yielding +/−40% error in water massflow. The gaserror is high at low GVF, dropping to within 3% for GVFs over 15%. Aswith the density and mass flow errors, higher data density (i.e. moreexperimental points) may generally allow improvement in the quality ofthe fit, and also may allow for a better assessment of the level ofexperimental noise.

FIGS. 55-63 are graphs illustrating a “3-dimensional” correction forliquid massflow and density, which takes into account variations in theerror due to variations in the water-cut measurement(s). This techniquemay be used to obtain acceptable errors over a wider range of water cuts(as opposed to the above examples, in which flow data reported on isgenerally limited to about 6% water cut).

Thus, in order to consider such variations in mass flow and densityerrors that are caused by variations in water cut measurement(s), FIGS.55-63 illustrate the use of a true water-cut reading as an extra inputparameter, alongside apparent drop in mixture density and apparentmassflow.

The data is based on the oil data discussed above, but with nominalwater-cut values of 0, 5.5, 13.1, 24.8, 35.6 and 49%. The distributionof flowlines per nominal water-cut is as follows:

0%: 4000 and 6000 bpd

5.5%: 3000, 4000, 6000 and 8000 bpd

13.1%: 3000 and 6000 bpd

24.8%: 3000 and 7000 bpd

35.6%: 3000 and 7000 bpd

49%: 3000 5000, 7000 and 8000 bpd

FIGS. 55A and 55B illustrate raw fluid mixture density and massflowerrors, respectively. FIGS. 56-61 illustrate residual fluid mixturemassflow errors after the previously used “6% water cut” model isapplied. It is apparent that while some of the errors (especially forthe 6% water cut data itself, FIG. 57) are small, at higher water cutsthe residual errors grow. Similar trends are shown for residual densityerrors using the 6% water cut data as the model.

Improved models for mixture density and massflow errors were trainedusing the true water-cut value as an extra input. The accuracy of theresulting corrections on the training data is given in FIGS. 62 and 63.The residual errors are greater than for a model based only on a singlewater cut (mass flow within 5% instead of 2%, density within 2% insteadof 1%). However, the model covers a good range of water cut readingsinstead of only a single value, and there represent a potentialimprovement over the worst errors in FIGS. 56-61.

The described errors may be reduced by having more data points. Forexample, for most of the water cuts there were only two flow lines. Thenumber of data points in the set may be insufficient to be able toidentify outliers. With more and better data quality, perhaps smallermass flow and density errors may be possible, even allowing for a rangeof water cut values.

FIGS. 64-68 are graphs illustrating results from embedding thethree-dimensional liquid massflow and density correction of FIGS. 55-63into the process described above with respect to FIGS. 50 and 54 andFIG. 27. By successive generations of the water-cut, density andmassflow corrections, volumetric errors resulting in the use of thismodel and the water cut error model may be shown.

Thus, FIGS. 64-68 illustrate results of successive corrections ofwater-cut, liquid(s), and gas massflow correction using the density andmassflow corrections that take into account the variations due towater-cut. The end results are calculations of volumetric flows for oil,water and gas, as may be used by, for example, the oil and gas industry.

These illustrated calculations represent a “complete” set, suitable foroil continuous applications. The data is based on the oil data asdescribed above, with nominal water-cut values of 0, 5.5, 13.1, 24.8,35.6 and 49%. The water-cut, massflow and density corrections used arebased on the whole data set for the range of water-cut from 0 to 50%.

The water cut correction model used is the same as is discussed abovewith respect to FIGS. 42-49. As already stated, the procedure employedis as described with respect to FIGS. 27 and 50-54, but the density andmassflow corrections used take into account the water-cut variations.The density and massflow correction models used are the ones discussedabove with respect to FIGS. 55-63.

FIG. 39, above, illustrates the raw gas-induced water-cut meter errors.FIGS. 64A, 64B, 65A, 65B, and 65C give the raw mixture density andmassflow gas-induced error, and raw water, oil and gas error,respectively. With the available data it is possible to converge insuccessive calculations, with the water-cut measurement corrected within5%, the mixture density mainly within 2% and massflow mainly within 5%,as shown in FIG. 66A-66C.

The water, oil and gas correction accuracies achieved after successivecalculations are shown in FIG. 67A-67C. The oil massflow is correctedmainly within 5%. The water volumetric flow is most affected, with 2-3%error in water-cut yielding +/−40% error in water volumetric flow. Thegas error is high at low GVF, as expected, dropping to mainly within 5%for GVFs over 15%.

FIG. 68 illustrates an example of the corrected water-cut behaviorduring the process(es). As with the density and mass flow errors, higherdata density (i.e. more experimental points) may allow improvement inthe quality of the fit, and may also allow a better assessment of thelevel of experimental noise.

A set of analysis tools and correction algorithms have been illustratedthat, given appropriate data for the oil, water, and gas used in aspecific application, may compensate for gas-induced errors in Coriolisand water cut readings, thereby to deliver volumetric gas, water and oilflow rates.

As described above, a massflow meter may be capable of maintainingoperation in the presence of a high percentage of gas in a measuredflow, both with a single or a mixed liquid (i.e., in two-phase orthree-phase flow). Estimates and/or apparent measurements of theliquid-gas mixture density and massflow may thus be obtained. However,these estimates have errors that depend on various factors, including,for example, the gas void fraction and/or the true liquid massflow,which may be so large as to render the raw measurements useless.

By using an additional measurement parameter, such as, for example, awater cut or gas void fraction measurement, along with the apparent massflow rate and density measurements, corrected values for all of theseparameters, and others, may be obtained. Moreover, by cycling throughthese measurements and calculations with ever-improved corrections,successively improved values may be obtained, as, for example, thecorrections converge to specific values.

As described above, techniques for performing these corrections may bebased on data-fitting techniques that seek to determine, for example,existing error rates in a particular setting or configuration, so thatthese errors may be accounted for in future measurements andcorrections. As such, these techniques may be dependent on an extent ofa correlation between the settings/configurations in which the data wasobtained, and the settings/configurations in which they are ultimatelyapplied.

Related or other correction techniques may be used that seek tocharacterize fluid flow(s) in a more general sense, i.e., using fluidflow equations that seek to describe a behavior of the flow as aphysical matter. For example, the well-known Navier-Stokes equations maybe used in this sense.

Specifically, the three-dimensional unsteady form of the Navier-Stokesequations describe how the velocity, pressure, temperature, and densityof a moving fluid are related. The equations are a set of coupleddifferential equations and may, in theory, be solved for a given flowproblem by using methods from calculus, or may be solved analytically,perhaps using certain simplifications or adjustments that may bedetermined to be helpful and applicable in a given circumstance.

These or related equations may consider, for example, convection (aphysical process that occurs in a flow of gas in which some property istransported by the ordered motion of the flow), and/or diffusion (aphysical process that occurs in a flow of gas in which some property istransported by the random motion of the molecules of the gas, and whichmay be related to the viscosity of the gas). Turbulence, and thegeneration of boundary layers, are the result of diffusion in the flow.

By using such fluid flow equations and characteristics, correctiontechniques may be obtained for many or all of the parameters andtechniques discussed above. For example, such fluid flow equations maybe used in defining a general correction model, which may besupplemented by data-fitting techniques such as those described above,or vice-versa.

A number of implementations have been described. Nevertheless, it willbe understood that various modifications may be made. Accordingly, otherimplementations are within the scope of the following claims.

1. A system comprising: a controller that is operable to receive asensor signal from a first sensor connected to a vibratable flowtubecontaining a three-phase fluid flow that includes a first liquid, asecond liquid, and a gas, the controller being further operable toanalyze the sensor signal to determine an apparent flow parameter of thefluid flow; a second sensor that is operable to determine an apparentflow condition of the fluid flow; and a corrections module that isoperable to input the apparent flow parameter and the apparent flowcondition and determine a corrected flow parameter therefrom. 2-35.(canceled)